Question

Prove that tangents from an external point are equal.

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Answer 1

Let PR and QR are tangent drawn from an external point

R to the circle

touching at points P and Q respectively.

Join OR

Proof:

In AOPR and AOQR,

OP=OQ (Radii of the same circle)

∠OPR =∠OQR (Since PR and QR are tangents to the

circle)

OR=OR (Common side)

△OPR = △OQR (By R.H.S)

∴PR = QR (C.P.C.T)

Thus, tangent drawn from an external point to a circle

are equal.

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Answer 2

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