In Fig. 9.19, the common tangent, AB and CD to two circles with centres O and O' intersect at E. Prove that the points O, E, O' are collinear.

A circle is touching the side BC of a △ABC at the point P and touching AB and AC produced at points Q and R respectively. Prove that AQ = 1/2 (Perimeter of △ABC).

TextDefinition of Tangent to a CircleTheorem on Equal Length of Tangents from External Point

In Fig.-2, if a circle touches the side QR of △PQR at S and extended sides PQ and PR at M and N, respectively, then prove that PM = 1/2 (PQ + QR + PR)

TextDefinition of Tangent to a CircleTheorem on Equal Length of Tangents from External Point

In Fig. 3, 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 6 cm and 8 cm respectively. If the area of △ABC is 84 cm², find the lengths of sides AB and AC.

TextDefinition of Tangent to a CircleTheorem on Equal Length of Tangents from External Point

The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC.

True/FalseDefinition of Tangent to a Circle