In the given figure, O is the centre of the circle.
If ∠AOB = 110° and ∠AOC = 80°, then ∠BAC = ?
75°
80°
85°
95°
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Question

In the given figure, O is the centre of the circle in which ∠OBA = 30° and ∠OCA = 40°. Then, ∠BOC = ? 1. 70° 2. 100° 3. 120° 4. 140°

KnowledgeBoat · Accepted Answer

Join BC. In △BOC, Since, OB = OC (Radius of same circle) ∴ ∠OBC = ∠OCB = x (let) By angle sum property of triangle, ⇒ ∠OBC + ∠OCB + ∠BOC = 180° ⇒ x + x + ∠BOC = 180° ⇒ ∠BOC = 180° - 2x In △AOC, By angle sum property of triangle, ⇒ ∠BAC + ∠CBA + ∠ACB = 180° ⇒ ∠BAC + (30° + x) + (40° + x) = 180° ⇒ ∠BAC + 70° + 2x = 180° ⇒ ∠BAC = 180° - 70° - 2x ⇒ ∠BAC = 110° - 2x We know that, The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference. ∴ ∠BOC = 2∠BAC ⇒ 180° - 2x = 2(110° - 2x) ⇒ 180° - 2x = 220° - 4x ⇒ 4x - 2x = 220° - 180° ⇒ 2x = 40° ⇒ x = = 20° ⇒ ∠BOC = 180° - 2x ⇒ ∠BOC = 180° - 2(20°) = 180° - 40° = 140°. Hence, option 4 is the correct option.

Mathematics

In the given figure, O is the centre of the circle in which ∠OBA = 30° and ∠OCA = 40°. Then, ∠BOC = ?
70°
100°
120°
140°

Circles

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In the given figure, ∠ABC and ∠DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 40°. Then, ∠BCD = ?
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In the given figure, O is the centre of the circle. If ∠OAC = 55°, then ∠OBD = ?
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In the given figure, O is the centre of the circle.
If ∠AOB = 110° and ∠AOC = 80°, then ∠BAC = ?
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95°

In the given figure, O is the centre of the circle and ∠OPQ = 30°. Then, ∠PAQ = ?
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Mathematics

In the given figure, O is the centre of the circle in which ∠OBA = 30° and ∠OCA = 40°. Then, ∠BOC = ?70°100°120°140°

Circles

Related Questions

In the given figure, ∠ABC and ∠DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 40°. Then, ∠BCD = ?60°40°100°80°

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In the given figure, O is the centre of the circle.If ∠AOB = 110° and ∠AOC = 80°, then ∠BAC = ?75°80°85°95°

In the given figure, O is the centre of the circle and ∠OPQ = 30°. Then, ∠PAQ = ?60°70°80°75°

In the given figure, O is the centre of the circle in which ∠OBA = 30° and ∠OCA = 40°. Then, ∠BOC = ?
70°
100°
120°
140°

In the given figure, ∠ABC and ∠DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 40°. Then, ∠BCD = ?
60°
40°
100°
80°

In the given figure, O is the centre of the circle. If ∠OAC = 55°, then ∠OBD = ?
55°
35°
45°
70°

In the given figure, O is the centre of the circle.
If ∠AOB = 110° and ∠AOC = 80°, then ∠BAC = ?
75°
80°
85°
95°

In the given figure, O is the centre of the circle and ∠OPQ = 30°. Then, ∠PAQ = ?
60°
70°
80°
75°