Multiple choice

Two chords AB and CD of a circle with centre 0 intersect each other at the point P. If $\angle $ AOD = $20^{\circ}$ and $\angle BOC = 30^{\circ}$, then $\angle $BPC is equal to:

  1. $50^{\circ}$
  2. $20^{\circ}$
  3. $25^{\circ}$
  4. $30^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Angle at center AOD = 20, BOC = 30. Angle at circumference subtended by arc AD is 10, arc BC is 15. The angle between chords intersecting at P is half the sum of angles subtended by the arcs at the center. Angle BPC = 1/2 * (Angle AOD + Angle BOC) = 1/2 * (20 + 30) = 25 degrees.