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14. Let be a right triangle: .

A circle has side as its diameter, meets hypotenuse at

A tangent line to at meets side at point

Prove that is isosceles.Code:F o \ θ'\ A o * \ | θ * *\ E | θ o | * * * | * \ θ ' * | * *\ * O * * \ * | * \ * | \ * | * \ * | * \ * | * \ θ' * C o * - - - - - - - o - - - - - - - - - - - - - - o B D

Draw radius

Since is isosceles.

. .

Since is tangent at

. . Hence, and are complementary.

. . Let

and are vertical angles: .

In and are complementary.

. . Hence: .

In

Therefore, is isosceles.