Give me the best and simple way for solving the question of class 9^{th} of Circles chapter of math of question no.6 how i solve this question in easy and simple way because it is very important type of question ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE, = AD.

AnilSinghBoraGuru

# ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE, = AD. Q.6

Share

Here, ABCE is a cyclic quadrilateral. In a cyclic quadrilateral, the sum of the opposite angles is 180Â°.

So, âˆ AEC+âˆ CBA = 180Â°

As âˆ AEC and âˆ AED are linear pair,

âˆ AEC+âˆ AED = 180Â°

Or, âˆ AED = âˆ CBA â€¦ (1)

We know in a parallelogram; opposite angles are equal.

So, âˆ ADE = âˆ CBA â€¦ (2)

Now, from equations (1) and (2) we get,

âˆ AED = âˆ ADE

Now, AD and AE are angles opposite to equal sides of a triangle,

âˆ´ AD = AE (proved).