Question

The lengths of tangents drawn from an external point to a circle are equal.

Answer 1

Yes, the statement is true. The lengths of tangents drawn from an external point to a circle are equal.

Answer 2

To prove :

The lengths of tangents drawn from an external point to a circle are equal i.e PQ = PR

Proof :

in Δ PQO And Δ PRO

$\star \: \sf \angle \: 1 = \angle \: 2 \: \: \{ \sf each \: 90\degree \} \\ \\ \star \: \sf PO = PO \: \: \{ \sf common \} \\ \\ \star \: \sf OQ = OR \ \: \: \{radius \: of \: same \: circle \}$

Therefore ,

$\sf\triangle \: PQO \: and \: \triangle PRO \: are \: similar \: triangle$

This gives ,

$\sf PQ = PR \: \: \{ CPCT \}$

Hence proved