Find AB given that B is the midpoint of DE, DE=20 and BC=25

Question

circle with two lines crossing 

Answer 1

Step 1. Place the elements

1. Let chords AC and DE intersect at B.
2. Since B is the midpoint of DE, we know:
3. DB=BE=20/2=10

So: DB=BE=10

Step 2. Use the Intersecting Chords Theorem

If two chords intersect inside a circle, then:

AB⋅BC=DB⋅BE

Step 3. Substitute values

AB⋅25=10⋅10

AB⋅25=100

AB=100/25=4

Final Answer:

AB=4