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Theorem 3

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: - In

From Theorem 3,

Again    [Linear Pair]

and       [Opposite angles of a cyclicquad]

       

 


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