Multiple choice

A circle in which CD has a length of 30 cm, acts as the longest chord of the circle. Points R and S lie on the circle such that the distance from R to D is 18 cm, and the length of segment CR is three times the length of segment CS. Then, the ratio of length of RD to CS is:

  1. 9 : 2

  2. 9 : 4

  3. 9 : 8

  4. 18 : 11
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B Correct answer
Explanation

CD is diameter (30cm). R, S on circle. RD=18. In right triangle CRD, CR = sqrt(30^2 - 18^2) = 24. CR = 3*CS, so CS = 8. Ratio RD:CS = 18:8 = 9:4.

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