Question

In the figure, chords AE and BC intersect each other at point D. If AD = BD, show that AE = BC.

Answer 1

Join AB.

If AD = BD  ...(i)

We know that:

AD × DE = BD × DC

But AD = BD

Therefore, DE = DC  ...(ii)

Adding (i) and (ii)

AD + DE = BD + DC

Therefore, AE = BC