Multiple choice

Two chords AB and CD of a circle intersect at point O inside the circle. It is given that AO = 1cm, AB = 13 cm, CD = 8 cm. What is the ratio between the larger and to smaller section among CO and OD ?

  1. 11 : 5

  2. 9 : 7

  3. 3 : 1

  4. 5 : 3
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C Correct answer
Explanation

By the intersecting chords theorem: AO × OB = CO × OD. Given AO = 1cm and AB = 13cm, so OB = AB - AO = 13 - 1 = 12cm. Therefore, AO × OB = 1 × 12 = 12. For CD = 8cm, let CO = x and OD = 8-x. Then x(8-x) = 12. Solving: x² - 8x + 12 = 0 gives x = 6 or x = 2. The larger section is 6cm, smaller is 2cm. Ratio = 6:2 = 3:1.

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