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`        If two sides of a cyclic quadrilateral are equal then prove that the other two sides are parallel to each other`
3 years ago

```							Let ABCD be the cyclic quadrilateral with AD parallel to BC. The center of the circle is O.  since AD is parallel to BC and AC is the transverseangle DAC = angle ACBangle DAC is subtended by chord DC on the circumference and angle ACB is subtended by chord AB. If the angles subtended by 2 chords on the circumference of the circle are equal, then the lengths of the chords is also equal. Hence, DC = AB i.e. the 2 remaining sides of the cyclic quadrilateral are equal.  Now, BD and AC are the 2 diagonals. In triangle ABD and triangle DCAAB = CD angle DCA = angle DAB (angles subtended by the same chord AD)angle ACB = angle DAC(proved above)Hence, triangle ABD is congruent to triangle DCA hence, BD = AC
```
3 years ago
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