Multiple choice

In $\displaystyle\Delta ABC,AD$ is perpendicular to $BC$ and $O$ is circumcentre of $\displaystyle\Delta ABC$, $\displaystyle \angle B=55^{\circ}, \angle A=80^{\circ}.$ Find $\displaystyle \angle OCB$

  1. 5$\displaystyle ^{\circ}$
  2. 10$\displaystyle ^{\circ}$
  3. 15$\displaystyle ^{\circ}$
  4. 20$\displaystyle ^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In triangle ABC, angle C = 180 - 80 - 55 = 45 degrees. The circumcenter O satisfies angle BOC = 2 * angle A = 160 degrees. In triangle BOC, OB = OC, so angle OCB = (180 - 160) / 2 = 10 degrees.

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