Mathematics
In the given figure, O is center of the circle. Chord BC = chord CD and angle A = 80°. Angle BOC is :
120°
80°
100°
160°
Answer
Given,
Chord BC = chord CD
∴ ∠BOC = ∠COD = x (let)
From figure,
∠BOD = ∠BOC + ∠COD = x + x = 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.
⇒ ∠BOD = 2∠BAD
⇒ 2x = 2 × 80°
⇒ x = 80°.
Hence, Option 2 is the correct option.
Related Questions
Arcs AB and BC are of lengths in the ratio 11 : 4 and O is center of the circle. If angle BOC = 32°, the angle AOB is :
64°
88°
128°
132°
In the given figure, AB is the side of regular pentagon and BC is the side of regular hexagon. Angle BAC is :
132°
66°
90°
120°
In the given circle, ∠BAD = 95°, ∠ABD = 40° and ∠BDC = 45°.
Assertion (A) : To show that AC is a diameter, the angle ADC or angle ABC need to be proved to be 90°.
Reason (R) : In △ADB,
∠ADB = 180° - 95° - 40° = 45°
∴ Angle ADC = 45° + 45° = 90°
(i) A is true, R is false
(ii) A is false, R is true
(iii) Both A and R are true and R is correct reason for A
(iv) Both A and R are true and R is incorrect reason for A
ABCD is a cyclic quadrilateral, BD and AC are its diameters. Also, ∠DBC = 50°.
Assertion (A) : ∠BAC = 40°.
Reason (R) : ∠BAC = ∠BDC = 180° - (50° + 90°) = 40°.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.