Solution of Triangles
and area of incircle of the triangle XYZ is then
If r, s and ∆ are the inradius, the semiperimeter and the area of triangle ABC, respectively, then what is the value of ?
Let r and R be the radius of the incircle and the circumcircle of a triangle respectively. If are the radii of the escribed circles opposite to the angles A, B and C respectively, then is
Let be the altitudes of triangle ABC from vertices A, B and C respectively such that , where Δ is the area of the triangle. Find the value of expression .
A pillar having a circular base and forming a part of a sphere of radius 80 cm is standing on a horizontal plane. Two points on the plane, which are at a distance of 100 cm and 60 cm from the base, have angular elevations of the highest point as α and β. What is the height of the pillar?
A boy is running in a circular ground. A pillar, which is inclined to the vertical, is standing in the centre of the ground. The greatest and least angles which the pillar subtends at boy’s eye are 60° and 45°. What is the angle subtended by the pillar when the boy is mid-way between the position?
The perpendiculars are drawn from the angles A, B and C of an acute angled triangle on the opposite sides, and produced to meet the circumscribing circle. These produced parts are respectively. What is the value of the expression ?
PQRS is a trapezium such that PQ is parallel to RS and ∠Q = 90°. If and then what is the value of RS?
A bird, moving in a straight line, passes vertically above two points A and B on a horizontal plane 800 m apart. The angle of elevation, as seen from B, when the bird is above A is 45°. However, the angle of elevation, as seen from A, when the bird is above B is 30°. What is the distance from A to the point at which the bird will touch the plane?
ABCD is a trapezium such that AB and CD are parallel and BC⊥CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to :
In a triangle PQR, P is the largest angle and Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
Let PQR be a triangle of area with and, where a, b and c are the lengths of the sides of the triangle opposite to the angles at P,Q and R respectively. Then equals
Let PQR be a triangle of area with and , where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R, respectively. Then equals
Match the List - I with List - II
|List - 1||List - 2|
|P. =||(1). 2|
|Q. If cos (A − B) = 77/85, a = 5, b = 4, then area of ∆ABC is
(∆ABC is acute angled triangle)
|R. If a = 5, b = 7, sin A = and sin (B + C) −
then k is
|S. If b + c = 3a, then cot cot is||(4). 5|
What is the perimeter of the triangle whose lengths of sides are three consecutive natural numbers and the largest angle is twice the smallest angle?
If the sides a, b, c of ΔABC are in the ratio 6 :7: 8, then what is the relationship between the radius of the circumcircle (R) and the radius incircle of the triangle (r)?