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In a circle with centre O, an arc ABC subtends an angle of 110° at the centre of the circle. The chord AB is produced to a point P. Then ∠CBP is equal to: (SSC CGL-2018)
- a)60°
- b)55°
- c)65°
- d)70°
Correct answer is option 'B'. Can you explain this answer?
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In a circle with centre O, an arc ABC subtends an angle of 110° at...
Given Information:
- Arc ABC subtends an angle of 110° at the centre O of the circle.
- Chord AB is produced to a point P.
To Find:
The measure of angle CBP.
Solution:
- The angle subtended by an arc at the centre of a circle is double the angle subtended by the same arc at any point on the remaining part of the circle.
- Therefore, angle ACB = 110° / 2 = 55°.
- Since angle ACB is an exterior angle of triangle CBP, angle CBP = angle ACB = 55°.
Therefore, the measure of angle CBP is 55°, which corresponds to option 'B'.
- Arc ABC subtends an angle of 110° at the centre O of the circle.
- Chord AB is produced to a point P.
To Find:
The measure of angle CBP.
Solution:
- The angle subtended by an arc at the centre of a circle is double the angle subtended by the same arc at any point on the remaining part of the circle.
- Therefore, angle ACB = 110° / 2 = 55°.
- Since angle ACB is an exterior angle of triangle CBP, angle CBP = angle ACB = 55°.
Therefore, the measure of angle CBP is 55°, which corresponds to option 'B'.
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Community Answer
In a circle with centre O, an arc ABC subtends an angle of 110° at...
Here, OA = OB (radius of the circle).
∴ ∠OAB = ∠OBA
In ΔOAB,
∠C = 180° – 55° = 125°
∠CBP = 180° - 125° = 55°
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In a circle with centre O, an arc ABC subtends an angle of 110° at the centre of the circle. The chord AB is produced to a point P. Then ∠CBP is equal to: (SSC CGL-2018)a)60°b)55°c)65°d)70°Correct answer is option 'B'. Can you explain this answer?
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