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Q 11. ABC and ADC are two right triangles with common hypotenuse AC. Prove that $\angle C A D=\angle C B D$..

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Given: ABC and ADC are two right triangles with common hypotenuse AC.

To prove : $\angle C A D=\angle C B D$

Proof :

Triangle ABC and ADC are on a common base BC and $\angle \mathrm{BAC}=\angle \mathrm{BDC}$.

Thus, points A, B, C, and D lie in the same circle.

(If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, four points lie on the circle.)

$\angle C A D=\angle C B D$ (Angles in the same segment are equal)

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