Q22 of 47 Page 1

Prove that the length of the tangents drawn from an external point to a circle ar equal.

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Given: PQ and PR are tangents from an external point P to the circle with centre O.


To prove: PQ = PR


Construction: Join O to P, Q, and R


Proof: In ΔOPQ and ΔOPR,


⇒ OQ = OR [radii of same circle]


⇒ OP = OP [Common]


∴ ΔOPQ ≅ ΔOPR [R.H.S.]


This gives, PQ = PR [By CPCT]


Ans. Hence, the length of the tangents drawn from an external point to a circle is equal.


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