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A B C and A D C are two right triangles ...

`A B C` and `A D C` are two right triangles with common hypotenuse `A Cdot` Prove that `/_C A D=/_C B Ddot`

Text Solution

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Since, `/_ABC` and `/_ADC` are 90.
These angles are in the semi-circle.
Thus, both the triangles are lying in the semi-circle and `AC` is the diameter of the circle.
Points `A`,`B`,`C` and `D` are concyclic.
Thus, `CD` is the chord.
Angles in the same segment of the circle are equal. Thus,
`/_CAD=/_CBD`
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