(Q2) Use Pythagaros theorem and write proof of above theorem "the lengths of tangents drawn from an external point to a circle are equal."

Given: Two tangents PA and PB to a circle with centre O, from an exterior point P.

R.T.P : PA =

PABO

Proof: In △OAP; ∠OAP = 90°

∴ AP2 = OP2 - O2

[∵ Square of the hypotenuse is equal to the sum of squares on the other two sides - Pythagaros theorem]

[∵ O = OB, radii of the same circle]

= BP2 [∵ In AOBP; OB2 + BP2 = OP2] [BP2 - OP2 - 2]

AP2 - 2

PA - Hence proved