# We have ABCD cyclic Convex quadrilateral HOW WE CAN PROVE THAT sinABD=sinADC?

##### 1 Answer

Apr 14, 2018

The assertion is not true.

#### Explanation:

I don't think we CAN prove that sinABD = sinADC. In fact, we can show that it is not necessarily true using some counter-examples.

Consider the three convex quadrilaterals inscribed in the same size circles below.

In all three cases angle ABD is the **same**, but angle ADC is **different**. How could their sines all be the same if this is the case?

Perhaps you don't mean "cyclic" quadrilateral.