Question

Two chords AB and CD of a circle intersect externally at E. If EC = 2 cm, EA = 3 cm, AB = 5 cm, find the length of CD.

Answer 1

Given:

EC = 2 cm

EA = 3 cm

AB = 5 cm

Two chords AB and CD intersect externally at point E.

Step 1: Find EB

Point B lies further on the same secant E–A–B.

EB = EA + AB

EB = 3 + 5

EB = 8 cm

Step 2: Use the External Secant Segment Theorem

For two secants from external point E:

EA × EB = EC × ED

Substitute known values:

3 × 8 = 2 × ED

24 = 2ED

Solve for ED:

ED = 24 ÷ 2

ED = 12 cm

Step 3: Find CD

ED consists of EC + CD:

ED = EC + CD

12 = 2 + CD

So,

CD = 12 − 2

CD = 10 cm