Question

Iwo opposite sides AB and DC of cyclic quadrilateral ABCD intersect in E when
produced. Prove that AEAD and AECB are similar.​

Answer 1

Answer:

ABCD is a cyclic quadrilateral in which diagonals AC and BD intersect in E at right angles , l is a line through E and perpendicular to AB meets CD in F. <br> We have

<br>

<br>

.....(1) <br>

<br> Again

<br> In

, we have <br>

<br>

.......(2) <br> From eqs.(1) and (2) , we get <br>

<br> But

(vertically opposite angles) <br>

<br> Also,

(angles in the same segment of a circle are equal) <br>

<br>

(sides opposite to equal angles of a triangle are equal) <br> Similarly ,

<br>

<br> Hence, F is the mid-point of CD.