Question

3. Chords AB and CD intersect inside a circle at point E. AE= 5, CE =10, EB = x, and ED = x-4. Find EB and ED.

Answer 1

we know that
When two chords intersect each other inside a circle, the products of their segments are equal (Intersecting Chord Theorem)
so
AE*EB=CE*ED
5*x=10*(x-4)
5x=10x-40
10x-5x=40
5x=40
x=40/5
x=8

therefore
EB=x----------> EB=8
ED=x-4---------> ED=8-4-----> ED=4