Question

TP and TQ are tangents from T to the circle with Centre O and R is any point on circle. If AB is the tangent to circle at R then prove that TA+AR=TB+BR​

Answer 1

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Answer 2

Tangents of the circle = TP and TQ (Given)

Centre of the circle = O  (Given)

The tangents drawn from an external point to the circle are always equal in length.

Let T be the external point which is equal in length thus,

TP = TQ    

= TA + AP = TB + BQ --- eq 1

Let A be the external point which is also equal in length, thus,

AP = AR --- eq 2

Let B be the external point, thus,

BQ = BR --- eq 3

Substituting the value of AP and BQ from equation 1, 2, and 3, -

TA + AR = TB + BR

Hence proved.