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On a common hypotenuse AB, two right ang...

On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated on opposite sides. Prove that `angleBAC=angleBDC`.

Text Solution

Verified by Experts

Clearly, `/_ACB = 90^(@) ` and `/_ ADB = 90^(@)`
Thus, the opposite angles of quad. ACBD are supplementary .
`:. ` ACBD is a cyclic quadrilateral.
This means that a circle passes through the points A,C,B and D
`:. /_BAC = /_ BDC [ /_ s` in the same segment].
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