Multiple choice

OC is perpendicular to the chord AB of a circle with center O.OC is produced to meet the circle in D.If AB = 8 cm. and CD = 2 cm., then the radius of the circle is -

  1. 4 cm.

  2. 6 cm.

  3. 5 cm.

  4. 8 cm.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

OC is perpendicular to chord AB, so C bisects AB. AC = 4 cm. Let radius = r, then OC = r - CD = r - 2. In right triangle OAC: OA² = OC² + AC², so r² = (r - 2)² + 4² = r² - 4r + 4 + 16. Cancelling r²: 0 = -4r + 20, giving r = 5 cm. This matches option C.

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