Angle Subtended by an Arc of a Circle on the Circle and at the Center

Q.

If O is the centre of the circle, find the value of x in each of the following figures:

Q.

In the given figure, O is the centre of a circle. If $\angle OAB={40}^{\circ }$ and C is a point on the circle then $\angle ACB=?$

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

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

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

(d) ${100}^{\circ }$

Q.

In the given figure, O is the centre of the circle. If $\angle ACB={50}^{\circ }$, find $\angle$OAB.

Q.

In the given figure, O is the centre of a circle and $\angle ACB={30}^{\circ }.\text{Then,}\angle AOB=?$

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

(b) ${15}^{\circ }$

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

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

Q.

In the given figure, O is the centre of a circle and $\angle AOC={120}^{\circ }.$ Then, $\angle$BDC = ?

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

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

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

(d) ${15}^{\circ }$

Q.

In the given figure, AB is a chord of a circle with centre O and AB is produced to C such that BC = OB. Also, CO is joined and produced to meet the circle D. If $\angle$ACD = $y^{\circ }$ and $\angle$AOD = $x^{\circ }$, prove that x = 3y.

Q.

Is a cross b equal to B cross A

Q.

In the figure, P and Q are centres of two circles intersecting at B and C. ACD is a straight line. Then $\angle BQD$ =

Q.

Angle formed in minor segment of a circle is

1. acute

2. Right angle

3. none of these

4. obtuse

Q.

In the given figure, $O$ is the center of a circle in which $\angle OAB={20}^{\circ }$ and $\angle OCB={50}^{\circ }.$ Then, $\angle AOC=?$

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

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

(c) ${20}^{\circ }$

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

Q.

In the given figure, O is the centre of a circle in which $\angle OBA={20}^{\circ }and\angle OCA={30}^{\circ }.\text{Then,}\angle BOC=?$

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

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

(c) ${100}^{\circ }$

(d) ${130}^{\circ }$

Q.

In the figure, it is given that O is the centre of the circle and $\angle AOC={150}^{\circ }$. Find $\angle ABC$.

Q.

In the given figure, O is the centre of the given circle and measure of arc ABC is ${100}^{\circ }.$ Determine $\angle ADCand\angle ABC$

Q.

In the figure, O and O' are centres of two circles intersecting at B aand C. ACD is a straight line, find x.

Q.

In the given figure, O is the centre of a circle and $\angle AOB={130}^{\circ }.Then,\angle ACB=?$

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

(b) ${65}^{\circ }$

(c) ${115}^{\circ }$

(d) ${155}^{\circ }$

Q.

In the figure, O is the centre of the circle.

Find $\angle BAC$.

Q.

In the given figure, O is the centre of the circle and arc ABC subtends an angle of ${130}^{\circ }$ at the centre. If AB is extended to P, find $\angle PBC.$

Q. Question 16
In figure, $\angle ACB={40}^{\circ }$. Find $\angle OAB$.

Q.

In the figure, $\Delta PQR$ is an isosceles triangle with PQ = PR and m $\angle PQR={35}^{\circ }$, Find m $\angle QSR$ and m $\angle QTR$

Q.

In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If $\angle ABC={25}^{\circ }$, calculate $\angle CED$.

Q.

In the figure, if $\angle AOB={80}^{o}and\angle ABC={30}^o$, then find $\angle CAO$.

Q.

In the given figure, O is the centre of the circle and $\angle \text{AOB}={70}^{\circ }$.

Calculate the values of (i) $\angle \text{OCA}\left(ii\right)\angle \text{OAC}.$

Q.

In the given figure, ABCD is a cylic quadrilateral in which BC = CD and $\angle CBD={35}^{\circ }.$ Then, $\angle BAD=?$

(a) ${65}^{\circ }$

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

(c) ${110}^{\circ }$

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

Q.

In the given figure, $\angle AOB={90}^{\circ }and\angle ABC={30}^{\circ }.Then,\angle CAO=?$

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

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

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

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

Q. Question 13
The circumcentre of the $\Delta ABC$ is O. Prove that $\angle OBC+\angle BAC={90}^{\circ }$.

Q.

(i) In Figure (1), O is the centre of the circle. If $\angle \text{OAB}={40}^{\circ }$ and $\angle \text{OCB}={30}^{\circ }$, find $\angle \text{AOC}$.

(ii) In Figure (2), A, B and C are three points on the circle with centre O such that $\angle \text{AOB}={90}^{\circ }$ and $\angle \text{AOC}={110}^{\circ }$. Find $\angle \text{BAC}$.

Q.

In the given figure, O is the centre of a circle and $\angle BOD={150}^{\circ }$. Find the values of x and y.

Q.

If A, B, C are three points on a circle with centre O such that $\angle AOB={90}^{o}and\angle BOC={120}^o,then\angle ABC=$

1. ${60}^o$

2. ${75}^o$

3. ${90}^o$

4. ${135}^o$

Q. In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If $\angle PRQ=l$ and $\angle OPQ=m,$ then $l+m$=___.

1. ${70}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${180}^{\circ }$

Q.

In the figure, O is the centre of the circle. If $\angle APB={50}^o$, find $\angle AOBand\angle OAB$.