Q22 of 141 Page 447

In the given figure, O is the centre of a circle and ∠AOC = 120°. Then, ∠BDC = ?

Given: ∠AOC = 120°


Construction: Join OD


We know that,


∠AOC = 2 × ∠ADC


120° = 2 ∠ADC


∠ADC = 60°


Here,


∠ADB = 90° (angle in a semicircle)


∠ADB = ∠ADC + ∠CDB = 90°


∠ADC + ∠CDB = 90°


60° + ∠CDB = 90°


∠CDB = 90° – 60°


∠CDB = 30°


∴ ∠BDC = 30°

More from this chapter

All 141 →
20

In the given figure, O is the centre of a circle. If ∠AOB = 100° and ∠AOC = 90°, then ∠BAC = ?

 21

In the given figure, O is the centre of a circle. Then, ∠OAB = ?

 23

In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠CDA = ?

 24

In the give figure, and are two intersecting chords of a circle. If ∠CAB = 40° and ∠BCD = 80°, then ∠CBD = ?