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Syllabus

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.

explain this some in a little easy maNNER.PLS EXPERTSS

Q.5) Given, PQ = 28 cm. Find the perimeter of $\u25b3$PLM.

prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.

PQ is a chord of length 8cm of a circle of radius 5cm. The tangent at P and Q intersect at a point T. Find the length TP?

CAN I GET THE CORRECT EXPLATION OF THIS EXAMPLE????

plz

two cubes have their volumes in the ratio 8:125.what is the ratio of their surface areas?

prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc

one circle has radius 5 and its centre (0,5). A second circle has radius of 12 and its centre (12,0). What is the length of the radius of a third circle which passes through the centre of the second circle and both the points of intersection of the first two circles.

A circle touches the side Bc of a triangle ABC at a point P and touches AB and AC when produced at Q and R respectively. Show that

prove that the length of the tangents drawn from an external point to a circle are equal, hence show that the centre lies on the bisector of the angle between the two tangents?

each other externally. A third circle with centre R is drawn to touch the first two circles and

one of their common internal tangents as shown in the figure.Then,the radius of the circle with centre R is

ab is a chord of length 16cm of a circle of radius 10 cm .the tangents at a and b intersect at point p.find the length of pa

xandy.

Two tangents TP and TQ are drawn to a circle with center O from an external point T. Prove that angle PTQ = 2 OPQ.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two. If the sides of the triangle are 2 cm, 3 cm, and 4 cm, find the diameter of the smallest circle.

(a) 1 cm

(b) 3 cm

(c) 5 cm

(d) 4 cm.

Please give the working also..Ab is a diameter and AC is a chord of a circle such that angle BAC =30 .If then tangent at C intersects AB produced in D,prove that BC=BD

The sides AB,BC,CA of triangle ABC touch a circle with centre o and radius r at P,Q,R respectively.Prove that

(1) AB+CQ= AC+BQ

(2) Area (triangle ABC) = 1/2 (perimeter of triangle ABC) x r (radius)

If an isosceles triangle ABC in which AB = AC = 6 cm is inscribed in a

A chord of circle of radius 10 cm subtends a right angle at the centre.Find the area of the corresponding minor segment and hence find the area of the major sector?

The radius of the incircle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6cm and 8 cm .Determine the other two sides of the triangle.The radii of two concentric circles are 13 cm and 8 cm . AB is a diameter of the bigger circle BD is tangent to the smaller circle touching it at D.Find the length of AD

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to the diameter of the circle, show that triangle APB is equilateral.

If a, b, c are the sides of a right triangle where c is the hypotenuse, then prove that radius r of the circle touches the sides of the triangle is given by r = a+b+c/2

A right Triangle ABC, circumscribes a circle of radius r, If AB and BC are of lenghts 8cm and 6cm respectively, find the value of r.

Two tangent segments PA and PB are drawn to a circle with centre O, such that angle APB= 120degree. Prove that OP=2AP.

x° +y°.IF ANGLE BETWEEN TWO TANGENTS DRAWN FROM A POINT P TO A CIRCLE OF RADIUS A AND CENTER O IS 60 DEGREE THEN PROVE THAT AP = A UNDER ROOT 3.

(1)is her finding correct?justify it . (2)find angle BAC if a =30

prove that the tangents drawn at ends of a diameter of a circle are parallel.

if pi is taken as 22/7, the distance (in m) covered by a wheel of diameter 35cm in one revolution is ....

PQR is a right angled triangle right angled at Q.PQ=5cm,QR=12cm.A circle with centre O is inscribed in triangle PQR, touching its all sides.find the radius of the circle.

From an external point P, two tangents PA and PB are drawn to a circle

Prove that the parallelogram circumscribing a circle is a rhombus. in this question do also have to prove that the diagonals are also equal?

two circles with centres O and O' of radii 3cm and 4cm respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles find the lenghth of the common chord PQ.

A circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm , BC = 7 cm and CD = 4 cm. Find AD.

if from any point on the common chord of two intersecting circles , tangents be drawn to the circles , prove that they are equal .

in the given figure TAS is a tangent to a circle with centre O.at the point A, if angle OBA=32

^{0}. find the value of x?PQ and RS are two parallel tangents to a circle with centre'O',another tangent AB with the point of contact 'C' intersecting PQ and RS at A and B respectively.Prove that angle AOB=90 degree.

^{0}[1]If PA and PB are tangents from an outside point P such that PA = 10 cm and angle APB = 60 .find the length of the chord AB.

[2]prove that the tangent drawn at the ends of a chord of a circle make equal with the chord.

[3]prove that the line segment joining the points of contact of two parallel tangent to a circle is a diameter of the circle.

the diameters of two circles are 38cm and 18cm.the diameter of the circle whose circumference is equal to sum of the circumference of the two circles is?

^{o},prove that 4(PS^{2}) = 3(OP^{2})Two circles touch externally at a point P and a common tangent touches them at A and B.Prove that AB subtends a right angle at P.

A quadrilateral is drawn to circumscribe a circle. Prove that sum of opposite sides are equal

Circle C(O,r) touches the circle C(o,r') internally at P. PB is a chord of larger circle, which intersects the smaller circle at A. Then prove that PA : PB = r : r'.

Tangents PQ and PR are drawn to a circle such that angle RPQ= 30 degreeA chord RS is drawn parallel to tangent PQ.

Find angle RQS...??? ANSFAST...

ab and cd are common tangents to two circles of unequal radii. prove that ab=cd

1) 2 circles touch internally at point P. From a point T on the common tangent at P, tangent segments TQ and TR are drawn to the circles. Prove that TQ =TR.

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that the triangle APB is equilateral.

Two circles touch internally at a point P and from a point T on the common tangent at P ,tangent segments TQ and TR are drawn to the 2 circles .Prove that TQ=TR.

In a right triangle ABC in which angle B = 90', a circle is drawn with AB as diameter intersecting the hypotenuse ACat P. Prove that the tangent to the circle at P visects BC.

In a triangle ABC, AB = 8cm, angle ABC = 90 degree. Then find the radius of the circle inscribed in the triangle.

prove that the parallelogram circumscribing a circle is a rhombus.???

PQ is tangent to outer circle and PR is tangent to inner circle. if PQ=4cm,OQ=3cm and OR=2cm then the length of PR is

a)5cm b)root21

c)4cm d)3cm

PAB is a secant and PT is a tangent. Prove that PA X PB =PT^{2}the difference of squares of two numbers is 180. the square of smaller no. is 8 times the larger number. find the two numbers .

PT to the circle and a line PB intersect

ing the circle at two points A and B are

drawn. If PA =8 cm, and PT = 12 cm

then length of PB is

A circle is inscribed in a triangle ABC, having sides 8 cm , 10 cm and 12 cm. Find AD , BE and CF ( these 3 are altitudes of triangle ABC).

(make sure to provide an appropriate diagram this time)Triangle ABC is isosceles in which AB=AC circumscribed about a circle. Prove that base is bisected by the point of contact.

in two concentric circles, prove that all chords of the outer circle which touches the inner circle are of equal lengths.

Two circles of radius r and r' touch externally at P. APB is a secant intersecting the circles respectively at A and B(other than P). Prove that PA/PB = r/r'

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O , at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of DO'/CO.....cAn aNy1 hElP MeH WiD thIs qUeStIoN pLs...???????

If from a external point P of a circle with centre O, two tangents PQ and PRare drawn such that angle of QPR=120. prove tht 2PQ=PO.

Circles C (O,r) and C(O', r'), (r r' ) touch internally at P. PQ is a chord of circle C (O,r) which intersect circle C (O' , r' ) at R. Show that OO'RQ is a Trapezium.

The tangent at pt C of a circle and a diameter AB when extended intersect at P.If angle PCA = 110 find angle CBA

If the angle between two radii of a circle is 130 then the angle between the tangents at the end points of a radii at their point of intersection is :

Q1) From an external point P, tangents PA and PB are drawn to a circle with cente O.If CD is the tangent to the circle at a point E and PA=14cm, find the perimeter of triangle PCD.

Q2) a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB=6cm, BC=7cm, and CD=4cm find AD.

if possible u pls. explain me these sums through video.

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If

prove that line segment joining the points of contact of two parallel tangents is the diameter of the circle

Prove that the angle between two tangents drawn from an external point to a circle is

supplementary to the angle subtended by the line segment joining the points of contact at the centre.

PQL and PRM are tangents to the circle with centre o at the points Q and R ,respectively and S is a point on the circle such that angle SQL=50 and angle SRM=60. Find angle QSR.

The tangent at a point C of a circle and diameter AB when extended intersect at P. If PCA=1100 , find CBA.6. The tangent at a point C of a circle and diameter AB when extended intersect at P. If PCA=1100 , find CBA.