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

## Trending Questions

**Q.**

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

30°

60°

90°

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 ∠ AOB = 80o and ∠ ACE = 10o. 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 ∠ CAB = xo; find (in terms of x) the values of :(i) ∠ COB, (ii) DOC, (iii)∠ DAC, (iv) ∠ ADC.

**Q.**

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

Given : ∠ AOC = a and ∠ 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 ∠ AOD = 60o, Calculate the numerical values of :

(i) ∠ ABD ,

(ii) ∠ DBC,

(iii) ∠ 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 ∠BAC=30∘. Show that BC is equal to the radius of the circumcircle of ΔABC, whose centre is O.

[3 MARKS]

**Q.**

In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ ABC + ∠ 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) ∠ AOB,

(ii) ∠ ACB,

(iii) ∠ 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 ∠BAC−∠OBC.

90∘

120∘

60∘

45∘

**Q.**

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT=40∘, ∠RPT=95∘ and ∠TSQ=75∘, find ∠SQT.

**Q.**

In the figure given below, AOB is a diameter of the circle and ∠ AOC=110∘. Find ∠ BDC.

35∘

30∘

20∘

90∘

**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 = 108o, find :

(i) ∠ CAB,

(ii) ∠ ADB.

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

- ∠x+∠y=∠z
- ∠y=∠z
- ∠x+2∠y=∠z
- 2∠x=∠z

**Q.**

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

If ∠ADC=32∘, 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.

100

^{o}70

^{o}80

^{o}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 ∠AOB = 110∘, then angle subtended by the arc at any point on the circle ∠APB is, where P is any point on the circle?

**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.

140∘

150∘

130∘

120∘

**Q.**

The given figure shown a circle with centre O. Also, PQ = QR = RS and ∠ PTS = 75o. Calculate :

(i) ∠ POS,

(ii) ∠ QOR,

(iii) ∠ 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 = 45^{0}, find ∠PQB

.

60

45

50

30

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 ∠BAC=30∘. 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?

Incentre

Inradius

Circumcentre

Circumradius

**Q.**

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

50°

40°

30°

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?