Question

Two chords $AB$ and $CD$ of circle whose centre is $O$, meet at the point $P$ and $\angle AOC={50}^o,\angle BOD={40}^o$. Then the value of $\angle BPD$ is:

• A. ${60}^o$
• B. ${40}^o$
• C. ${45}^o$
• D. ${75}^o$

Answer 1

Answer: (C)

${45}^o$

$\angle AOC+BOD=2\angle ABC+2\angle BCD$

$=2\angle ABC+\angle BCD$

$=2\angle BPD$......

( since, angle formed on major arc is half of the angle formed on center)

$\therefore \angle AOC+\angle BOD=2\angle BPD$

$2\angle BPD={50}^o+{40}^o$

$\angle BPD=\frac{{90}^o}{2}={45}^o$