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Question

ABC and ADC are two right triangles with common hypotenuse AC. Prove that CAD=CBD.


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Solution

Proving CAD=CBD:

From figure, it is clear that,

ABC=ADC=90, which means

These angles are in the semicircle.

Therefore both triangles ABC and ADC are lying in the semicircle.

AC is the diameter of circle with center O.

Therefore, Points A, B, C and D are concyclic means all the points lie on the circle.

Thus, CD is a chord.

Therefore, CAD=CBD (Angles in the same segment of the circle)

Hence Proved.


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