Question

31.
Prove that “the lengths of tangents drawn from an external point to a circle
are equal”.
​

Answer 1

Given : AB and AC are tangents of a circle.

BO and CO are radii of circle

To proof : AB = AC

Proof : In ΔABO and ACO

AO = AO (Common)

BO = CO (radii of same circle)

∠1 =∠2 ( radius is perpendicular to tangent)

Therefore ΔABO ≅ ACO (RHS congruent criteria)

Thus, AB = AC

HENCE PROVED

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