Ptolemy's Theorem and Cyclic Quadrilateral

[brisk11228]

1. The problem statement, all variables and given/known data
In cyclic quadrilateral ABCD with diagonals intersecting at E, we have AB=5, BC=10, BE=7, and CD=6. Find CE.

2. Relevant equations
Ptolemy's Theorem: The product of the measures of its diagonals is equal to the sum of the products of the measures of the pairs of opposite sides.

3. The attempt at a solution
I drew the picture and that's as far as I got.

[sankalpmittal]

1. The problem statement, all variables and given/known data
In cyclic quadrilateral ABCD with diagonals intersecting at E, we have AB=5, BC=10, BE=7, and CD=6. Find CE.

2. Relevant equations
Ptolemy's Theorem: The product of the measures of its diagonals is equal to the sum of the products of the measures of the pairs of opposite sides.

3. The attempt at a solution
I drew the picture and that's as far as I got.

Hint : First prove that ΔDEC is similar to ΔAEB by axiom AAA. To prove them similar , you have to apply theorem related to angles subtended by same segment or arc on circumference. Do you know what does that theorem state ?