AM-2459

Congruence and similarity proofs

A Math · Secondary 4 · Hard · Congruence and similarity proofs

In a circle with centre O, points A and B lie on the circle. The tangent at A and the tangent at B meet at an external point T. Which statement justifies that triangles

TAO

and

TBO

are congruent?

$TA = TB,\ OA = OB,\ OT$ common, so SSS congruence
$\angle TAO = \angle TBO$ only, so they are congruent
$TA = AO = BO$ , so they are congruent by SAS
$OT$ is a diameter, so all triangles with OT are congruent

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