Question

prove that tangents drawn to a cricle from an external point are eqaul​

Answer 1

To Prove:-

• The tangents drawn to a circle from an exterior point are always equal.

Proof:-

• Let a circle be with centre O.

• The tangents to the circle be PA and PB drawn from an exterior point P.

• The radius of the circle are OA and OB.

So we have to prove that PA = PB.

Now,

From the figure we get:-

❀ In triangle POB and POA,

$\tt\mapsto OA = OB. \\ \\ \tt(same \: \: radii \: \: of \: \: the \: circle). \\ \\ \rm\mapsto OP = OP. \\ \\ \rm(common). \\ \\ \tt\mapsto\angle PBO = \angle PAO = 90\degree. \\ \\ \rm(angles \: \: subtended \: \: by \: \: the \: \: tangent \: \:and \: \: radius \: \: of \: \: the \: \: crcle). \\ \\ \tt\longrightarrow so \: \: by \: \: RHS \: \: criteria \: \: we \: \: get \\ \\ \tt\leadsto \triangle POA \cong \triangle POB.$

$\tt\therefore$ PA = PB [By CPCT].

...HENCE PROVED...