Multiple choice

Two chords, AB and CD, of a circle intersect at O. If CO = 4 cm, OD = 3.75 cm and AB = 8 cm, then what is the length (in cm) of the smaller among AO and OB?

  1. 5.25

  2. 3

  3. 2.75

  4. 5

  5. NA
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio of boys to girls is 4:6, which simplifies to 2:3. Total students = 50, so boys = 20 and girls = 30. Using the weighted average formula: (20 * B + 30 * 60) / 50 = 62. Solving for B: 20B + 1800 = 3100, so 20B = 1300, B = 65.

AI explanation

By the intersecting chords theorem, AO multiplied by OB equals CO multiplied by OD. Substituting the known values gives AO multiplied by OB equal to 15, and since AB is 8 cm, OB is 8 minus AO. Solving the equation AO multiplied by (8 minus AO) equals 15 yields a quadratic equation where AO is 5 cm or 3 cm. The smaller of the two segments is therefore 3 cm.

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