Multiple choice

2 perpendicular chords AB and CD of a circle intersect at O (inside the circle). AB is bisected at O. If AO = 4 units and OD = 6 units. Find circumradius of $\displaystyle \bigtriangleup ACO $.

  1. $\displaystyle \sqrt{13} $
  2. $\displaystyle \frac{2\sqrt{13}}{3}$
  3. $\displaystyle \frac{\sqrt{15}}{2}$
  4. $\displaystyle \frac{2\sqrt{15}}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a circle, if two chords intersect at O, AO * OB = CO * OD. Since AB is bisected at O, AO = OB = 4. Thus, 4 * 4 = CO * 6, so CO = 16/6 = 8/3. Triangle ACO is right-angled at O. The hypotenuse AC = sqrt(AO^2 + CO^2) = sqrt(16 + 64/9) = sqrt(208/9) = 4*sqrt(13)/3. The circumradius of a right triangle is half the hypotenuse, which is 2*sqrt(13)/3.

Keep practicing — related questions