Q. 83.5( 4 Votes )

On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that BAC = BDC.

Answer :

Given: ACB and ADB are two right triangles.


To Prove: BAC = BDC


Since ACB and ADB are right angled triangles, therefore


C + D = 90° + 90°


= 180°


Therefore ADBC is a cyclic quadrilateral. ( Sum of opposite angles of a cyclic quadrilateral is 180°.)


Also, BAC and BDC lie in the same segment BC and angles in the same segment of a circle are equal.


BAC = BDC.


Hence Proved.


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