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

Q.

An equilateral triangle ABC is inscribed in a circle with centre O. Then, $\angle BOC$ is equal to:

1. 30°

2. 60°

3. 90°

4. 120°

Q.

In the given figure, AC is the diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q and r in terms of x.

Q.

In the given figure, AC the diameter of the circle with centre O. CD and BE are parallel. Angle $\angle$ AOB = ${80}^o$ and $\angle$ ACE = ${10}^o$. Calculate :

(i) Angle BEC,

(ii) Angle BCD,

(iii) Angle CED.

Q.

In the given figure, AOB is a diameter and DC is parallel to AB. If $\angle$ CAB = $x^o$; find (in terms of x) the values of :(i) $\angle$ COB, (ii) DOC, (iii)$\angle$ DAC, (iv) $\angle$ ADC.

Q.

The figure given below, shows a circle with centre O.

Given : $\angle$ AOC = a and $\angle$ ABC = b.

(i) Find the relationship between a and b.

(ii) Find the measure fo angle OAB, if OABC is a parallelogram.

Q.

AB is the diameter of the circle with centre O. OD is parallel to BC and $\angle$ AOD = ${60}^o$, Calculate the numerical values of :

(i) $\angle$ ABD ,

(ii) $\angle$ DBC,

(iii) $\angle$ ADC.

Q.

The angle subtended by the semicircle of a circle, on the circumference of the circle is __.

Q.

The figure shown a circle with centre O AB is the side of regular pentagon and AC is the side of regular hexagon.

Find the angles of triangle ABC.

Q.

In the figure, ABC is a triangle in which $\angle BAC={30}^{\circ }$. Show that BC is equal to the radius of the circumcircle of $\Delta ABC$, whose centre is O.
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Q.

In the given figure, AE is the diameter of the circle. Write down the numerical value of $\angle$ ABC + $\angle$ CDE. Give reasons for your answer.

Q.

In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. Calculate the sizes of :

(i) $\angle$ AOB,

(ii) $\angle$ ACB,

(iii) $\angle$ ABC.

Q.

In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of $\angle BAC-\angle OBC$.

1. ${90}^{\circ }$

2. ${120}^{\circ }$

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

4. ${45}^{\circ }$

Q.

In the given figure, if lines PQ and RS intersect at point T, such that $\angle PRT={40}^{\circ },\angle RPT={95}^{\circ }and\angle TSQ={75}^{\circ }$, find $\angle SQT.$

Q.

In the figure given below, AOB is a diameter of the circle and $\angle AOC={110}^{\circ }$. Find $\angle BDC$.

1. ${35}^{\circ }$

2. ${30}^{\circ }$

3. ${20}^{\circ }$

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

Q.

In the figure, O is the centre of the circle and the length of are AB is twice the length of are BC. If angle AOB = ${108}^o$, find :

(i) $\angle$ CAB,

(ii) $\angle$ ADB.

Q. In the given figure, O is the centre of the circle. Which of the following option is correct?

1. $\angle x+\angle y=\angle z$
2. $\angle y=\angle z$
3. $\angle x+2\angle y=\angle z$
4. $2\angle x=\angle z$

Q.

In the given figure, AB is the diameter of the circle with centre O.

If $\angle ADC={32}^{\circ },$ find angle BOC.

Q. In square ABCD , diagonals meet at O. P is a point on BC such that AB is equal to BP .find out angle POC, angle BDC and angle BOP.

Q.

In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If angle BOD = 160°, find the measure of angle BAD.

1. 100^o

2. 70^o

3. 80^o

4. 90^o

Q.

O is the centre of the circle. AB is a minor arc of the circle. The angle subtended by AB at centre $\angle$AOB = ${110}^{\circ }$, then angle subtended by the arc at any point on the circle $\angle$APB is, where P is any point on the circle?

1. 
2. 

3. 

4. 

Q.

In the given figure, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.

1. ${140}^{\circ }$

2. ${150}^{\circ }$

3. ${130}^{\circ }$

4. ${120}^{\circ }$

Q.

The given figure shown a circle with centre O. Also, PQ = QR = RS and $\angle$ PTS = ${75}^o$. Calculate :

(i) $\angle$ POS,

(ii) $\angle$ QOR,

(iii) $\angle$ PQR.

Q. Given-1) PQRST is cyclic polygon 2)O is center of the circle 3)PR=QR=RS 4) angle PQR=128 degree To find- angle PTQ, angle PTS, angle ROS.

Q. In the given figure, AC is a diameter of the circle. Find the value of $x.$

Q.

In the given figure, O is the centre of the circle & ∠PBA = 45⁰, find ∠PQB

.

1. 60

2. 45

3. 50

4. 30

5. 25

Q. in the circle angle PQR = 100 where P, Q and R are the points on the circle with centre O then find angle OPR

Q.

In the given figure, ABC is a triangle in which $\angle BAC={30}^{\circ }.$ Show that BC is equal to the radius of the circumcircle of the triangle ABC, whose centre is O.

Q.

What is the point of intersection of angle bisectors of a triangle called?

1. Incentre

2. Inradius

3. Circumcentre

4. Circumradius

Q.

In the given figure, O is the centre of the circle. Find $x$.

1. 50°

2. 40°

3. 30°

4. 20°

Q. What is the length (in terms of π) of the arc that subtends an angle of 36° at the centre of a circle of radius 5 cm?