Angle Subtended by Diameter on the Circle

Q.

In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

Q.

In the given figure, O is the centre of a circle. If $\angle OAC={50}^{\circ }\text{then}\angle ODB=?$

(a) ${40}^{\circ }$

(b) ${50}^{\circ }$

(c) ${60}^{\circ }$

(d) ${75}^{\circ }$

Q.

In the given figure, $BOC$ is a diameter of a circle and $AB=AC.$ Then, $\angle ABC=?$

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${90}^{\circ }$

Q.

What is the angle subtended by the diameter AB at the circumference of the circle?

1. Data inadequate

2. ${90}^{\circ }$

3. ${45}^{\circ }$

4. ${60}^{\circ }$

Q.

In the figure, O is the centre of the circle and $\angle BDC={42}^o$. The measure of $\angle ACB$ is

1. ${42}^o$

2. ${48}^o$

3. ${58}^o$

4. ${52}^o$

Q.

In the given figure, O is the centre of the circle and $\angle BCO={30}^{\circ }$. Find x and y.

Q.

In the given figure, O is the centre of the circle and $\angle DAB={50}^{\circ }.$ Calculate the values of x and y.

Q.

In the given figure, PQ is a diameter of a circle with centre O. If $\angle PQR={65}^{\circ },\angle SPR={40}^{\circ }and\angle PQM={50}^{\circ },\text{find}\angle QPR,\angle QPMand\angle PRS$

Q.

In the given figure, O is the centre of the circle. If $\angle$ABD=35${}^{\circ }$ and $\angle$BAC=70${}^{\circ }$, find $\angle$ACB.

Q.

In the figure, AOC is a diameter of the circle and arc $AXB=\frac{1}{2}$ arc BYC. Find $\angle BOC$.

Q.

The angle in a semicircle measures

(a) ${45}^{\circ }$

(b) ${60}^{\circ }$

(c) ${90}^{\circ }$

(d) ${36}^{\circ }$

Q.

In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If $\angle AEB={110}^{\circ }and\angle CBE={30}^{\circ }then\angle ADB=?$

(a) ${70}^{\circ }$

(b) ${60}^{\circ }$

(c) ${80}^{\circ }$

(d) ${90}^{\circ }$

Q.

In the given figure, AB is a diameter of a circle with centre O and DO||CB.

If $\angle BCD={120}^{\circ },$ calculate

(i) $\angle$BAD, (ii) $\angle$ABD,

(iii) $\angle$CBD, (iv) $\angle$ADC.

Also, show that $△$AOD is an equilateral triangle.

Q.

On a semi circle with $AB$ as diameter, a point $C$ is taken so that $\angle CAB={30}^{\circ }$. Find $\angle ACB\text{and}\angle ABC.$

Q.

In the given figure, BOC is a diameter of a circle with centre O. If $\angle BCA={30}^{\circ }\text{then}\angle CDA=?$

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${50}^{\circ }$

Q. Question 1
Prove that line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Q.

In the given circle, with AB as a diameter, find the value of x.

1. 60°

2. 40°

3. 50°

4. 30°

Q.

In the given figure, O is the centre of the circle, BD = OD and CD$\perp$AB. Find $\angle$CAB.

Q.

Question 10
If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Q.

In the given figure, AB is the diameter of the circle. Find the value of $x$.

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${90}^{\circ }$

Q.

In the figure, O is the centre of a circle and PQ is a diameter. If $\angle ROS={40}^{\circ }$, find $\angle RTS$.

Q. The value of x in the following figure is _____.

1. 60°

2. 35°

3. 45°

4. 45°

Q.

Given a circle with the center O. Find x.

1. 30°

2. 40°

3. 50°

4. 100°

Q. In the given figure, O is the centre of a circle. If ∠OAB = 40°, then ∠ACB = ?
(a) 40°
(b) 50°
(c) 60°
(d) 70°

Q.

Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

Q. In the given figure, O is the centre of a circle. If ∠OAC = 50°, then ∠ODB = ?
(a) 40°
(b) 50°
(c) 60°
(d) 75°

Q. 3.P is the centre of the circle. Prove that angle XPZ=2(angle YXZ+angle YZX)

Q. If a wheel has 6 spokes equally spaced , then find the measure of the angle between two adjacent spokes
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Q. 1. Find angle CAB , in the figure, if AOB is a diameter , C is any point on the circle and angle B =40 degrees

Q. Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).