If o is the centre of circle find x
Asked by admin @ in Math viewed by 358 People
If O is the centre of the circle, find the value of x in each of the following figures :
Answered by admin @
Given: O is the center of the circle.
To find : The value of x .
Solution :
(i) From figure : ∠AOC = 135° , ∠COB = x
∴ ∠AOC + ∠BOC = 180°
[Linear pair]
135° + ∠BOC = 180°
∠BOC = 45°
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∴ ∠BOC = 2 ∠COB
45° = 2x
x = 45°/2
x = 22½°
Hence x is 22½°
.
(ii) From figure : ∠ABC = 40° , ∠CDB = x
We know that angle in semi-circle is 90°.
∠ACB = 90°
In ∆ ABC,
Since Sum of the angles of a triangle is 180° :
∴ ∠CAB + ∠ACB + ∠ABC = 180°
∠CAB + 90° + 40° = 180°
∠CAB + 130° = 180°
∠CAB = 180° - 130°
∠CAB = 50°
Now,
Since angles in the same segment of a circle are equal :
∴ ∠CDB = ∠CAB
x = 50°
Hence x is 50°.
(iii) From figure : ∠AOC = 120° , ∠CBD = x
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∠AOC = 2 ∠APC
120° = 2 ∠APC
∠APC = 120°/2
∠APC = 60°
Since, APCB is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
∴ ∠APC + ∠ABC = 180°
60° + ∠ABC = 180°
∠ABC = 180° - 60°
∠ABC = 120°
∠ABC + ∠DBC = 180°
[Linear pair]
120° + x = 180°
x = 180° - 120°
x = 60°
Hence x is 60°.
HOPE THIS ANSWER WILL HELP YOU…..
Similar questions :
In Fig. 16.120, O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB.
In Fig. 16.122, O is the centre of the circle. Find ∠BAC.
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