Two chords AB and CD of circle whose centre is O, meet at the point P inside the circle such that ∠AOC = 50°, ∠BOD = 40°. Then the value of ∠BPD is
Explanation:
Let us join BC.
Now, ∠ABC = ½∠AOC = 25° (angle subtended by chord AC on circle is half of the angle it subtends at the center)
similalry, ∠DCB = ½∠DOB = 20° (angle subtended by chord AC on circle is half of the angle it subtends at the center)
In triangle, BPC, ∠BPD = ∠PCB + ∠PBC (exterior angle is sum of two opposite interior angles)
⇒ ∠BPD = 25° + 20° = 45°
Hence, option (c).
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