Sir,are all justifications of cons chap equally imp.Is there any justification for that drawing tangents to circles part? If there plz help me.Please reply as quick as possible
I guess your doubt is that "justification of construction of a pair of tangents from an external point without using centre."
Because normally doubt arises here :
Solution:
Now justification for such problem does not arises. But keep in mind the case is -construction of a pair of tangents from an external point without using centre.
Second type where justification is needed:
Draw a circle with thehelp of a bangle. Take a point outside the circle. Construct the pairof tangents from this point to the circles. Give the justification ofthe construction.
Solution:
The required tangents can be constructed on the given circle as follows.
Step 1
Draw a circle with the help of a bangle.
Step 2
Take a point P out side this circle and take two chords QR and ST.
Step 3
Draw perpendicular bisectors of these chords. Let them intersect each other at point O.
Step 4
Join PO and bisect it.Let U be the mid-point of PO. Taking U as centre, draw a circle of radius OU, which will intersect the circle at V and W. Join PV and PW.
PV and PW are therequired tangents.
Justification
The construction can be justified by proving that PV and PW are the tangents to the circle.For this, first of all, it has to be proved that O is the centre of the circle. Let us join OV and OW.
We know that perpendicular bisector of a chord passes through the centre.Therefore, the perpendicular bisector of chords QR and ST pass through the centre. It is clear that the intersection point of these perpendicular bisectors is the centre of the circle. ∠PVOis an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.
∴ ∠PVO =90°
⇒ OV ⊥PV
Since OV is the radius of the circle, PV has to be a tangent of the circle. Similarly, PW isa tangent of the circle.