A trapezium (with and ) is inscribed in a circle

MATHEMATICS · Multi-part · ICSE · Mathematics · Geometry · Geometry

Problem

A trapezium

ABCD

(with

AB \parallel CD

and

AD \neq BC

) is inscribed in a circle. The diagonals

AC

and

BD

intersect at

E

. It is given that

AB = 10\,\text{cm}

CD = 6\,\text{cm}

and

BE = 4\,\text{cm}

. (i) Prove that

\triangle AEB \sim \triangle CED

. (ii) Using part (i), show that

AE \times EC = BE \times ED

. (iii) Establish that

\angle AED = \angle ABD

. (iv) Calculate the length of

ED