Multiple choice

A chord AB is at a distance of 5 cm from the centre of the circle with a diameter of 26 cm. Another chord CD intersects with chord AB at E, such that AE ∶ EB = 5 ∶ 1 and CE ∶ ED = 4 ∶ 1. Find the length of the CD.

  1. 5√5 cm

  2. 10√5 cm

  3. 15√5 cm

  4. 20√5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using intersecting chords theorem and power of point: AB is 5cm from center, diameter 26cm so radius 13cm. AB length = 2√(13² - 5²) = 2√144 = 24cm. With AE:EB = 5:1, AE = 20cm, EB = 4cm. For chord CD through E with CE:ED = 4:1, using power of point E, the length CD = 10√5 cm. Option B is correct.

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