Question

Prove that if a chord is drawn from a point of contact of the tangent of the circle then angle made by this chord with the tangent are equal to the respective alternate angles made by segments with this chord

Answer 1

Step-by-step explanation:

Theorem 3. If a line touches a circle and from the point of contact a chord is drawn, the angle which this chord makes with the given line are equal respectively to the angles formed in the corresponding alternate segments.

Given:- PQ is a tangent to circle with centre O at a point A, AB is a chord and C, D are points in the two segments of the circle formed by the chord AB.

To Prove:- (i)

(ii)

Construction:- A diameter AOE is drawn. BE is joined.

Proof: - Iin

From Theorem 3,

Again [Linear Pair]

and [Opposite angles of a cyclicquad]