If o is the center of the circle find
Asked by admin @ in Math viewed by 432 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.
Similar Questions
If o is the centre of circle find x
Asked by admin @ in Math viewed by 359 persons
If O is the centre of the circle, find the value of x in each of the following figures :
Find the center and radius of each circle
Asked by maham237 @ in Mathematics viewed by 316 persons
Give the center, radius, and equation of the circle in the graph.
Finding center and radius of a circle from an equation
Asked by admin @ in Mathematics viewed by 305 persons
Determine the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1) by following the steps below. Use the distance formula to determine …
Find the measures of the indicated angles in circle o
Asked by maham237 @ in Mathematics viewed by 377 persons
Which statement is NOT true? (The figure is not drawn to scale.)
b = 106
d = 37
a = 53
c = 73
What is the general form of the equation for the given circle centered at o(0, 0)?.
Asked by maham237 @ in Mathematics viewed by 473 persons
What is the general form of the equation for the given circle centered at O(0, 0)?
a) x2 + y2 + 41 = 0
b) x2 + y2 − 41 …
What is the general form of the equation for the given circle centered at o(0, 0)?
Asked by maham237 @ in Mathematics viewed by 376 persons
What is the general form of the equation for the given circle centered at O(0, 0)?
a) x2 + y2 + 41 = 0
b) x2 + y2 − 41 …
How to identify the center and radius of the circle
Asked by admin @ in Mathematics viewed by 349 persons
Identify the center and the radius of a circle with equation (x-4)^2+(y+2)^2=9
Find the mass and center of mass of the lamina
Asked by admin @ in Mathematics viewed by 297 persons
Calculate the moments Mx and My and the center of mass of a lamina with the given density and shape.
ρ = 3
How to find area of a sector of a circle
Asked by admin @ in Mathematics viewed by 371 persons
The area A of a sector of a circle is given by A=πr²s/360, where r is the radius of the circle and s is the angle measure(in degrees) of the …
How to find the area of a circle without radius
Asked by admin @ in Mathematics viewed by 330 persons
How do i find the circumference of a circle without the radius given?
How do you find out the volume of a circle
Asked by admin @ in Mathematics viewed by 329 persons
Find the volume of a sphere with a great circle area of 201.06 square inches
An angle whose vertex is the center of a circle
Asked by admin @ in Mathematics viewed by 312 persons
An angle whose vertex is at the center of a circle is a middle angle of that circle.
A. True
B. False
Find the centre of the circle passing through
Asked by admin @ in Math viewed by 299 persons
find the centre of a circle passing through the points (3,-7),(3,3),(6,-6). want the answer for 4 marks
Find the area of square inscribed in a circle
Asked by admin @ in Math viewed by 338 persons
Find the area of square inscribed in a circle of radius 8cm?
O is the centre of circle of radius 5cm
Asked by admin @ in Math viewed by 293 persons
In figure O is the centre of a circle of radius 5 cm.T is a point such that OT=13CM and OT intersects the circle at E.if AB is the tangent …
Most viewed questions in Math
Prachi excellence in mathematics class 7 solutions pdf free download
Asked by admin @ in Math viewed by 12061 persons
Oxford new enjoying mathematics class 7 solutions chapter 1
Asked by admin @ in Math viewed by 11540 persons
Survey of various types of bank accounts icse project
Asked by admin @ in Math viewed by 11514 persons
Rahul went to his mother's mother in law
Asked by admin @ in Math viewed by 4186 persons