Angle in a Semicircle

Q.

Any angle whose vertex is at the centre of the circle is called

1. Reflex angle

2. Central angle

3. Straight angle

4. Right angle

Q.

What is the angle subtended by the diameter on the circumference of the circle?

1. 90º

2. 45º

3. Data inadequate

4. 60⁰

Q. Mr X is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. [4 MARKS]

Q.

Diameter of a circle is 30 cm. If the length of a chord is 20 cm, find the distance of the chord from the centre.

1. 12 cm

2. 

3. 

4. 

Q.

Find the number of right angles turned through by the hour hand of a clock, when it goes from $3to9$.

Q.

In the above figure O is the center of the circle and $\angle$AOB = ${80}^{\circ }$, then complete the matching.

$\begin{array}{cc}\text{Angle}& \text{Value}\\ \text{1.ACB}& \text{a.}{90}^0\\ \text{2.ADB}& \text{b.}{40}^0\\ \text{3.ABC}& \text{c.}{80}^0\\ \text{4.AOC}& \text{d.}{180}^0\end{array}$

1. 1- b, 2- b, 3-a, 4 -d

2. 1- b, 2- a, 3-c, 4 -d

3. 1- a, 2- d, 3-c, 4 -b

4. 1- a, 2- c, 3-d, 4 -b

Q.

In the following figure if O is the centre of the circle, AC = 5 cm and BC = 12 cm, then the radius of the circle is

1. 7.5 cm

2. 12 cm

3. 13 cm

4. 6.5 cm

Q. In the given figure, A, B and C are three points on a circle with centre O such that $\angle BOC={30}^{\circ }$ and $\angle AOB={60}^{\circ }$. If D is a point on the circle other than the arc ABC, find $\angle ADC$.

1. $(\frac{90}{2}{)}^{\circ }$
   
2. ${45}^{\circ }$
3. $(\frac{60}{2}{)}^{\circ }$
4. ${30}^{\circ }$

Q.

Pavan was wondering if he can find angle subtended between the hour hand and minute hand. So, he decided to find the angle between hour hand and minute hand when the clock shows 2 p.m. What do you think about the value of angle (in degrees)?

Ans:___

Q.

In triangle ABC, D is a point in AB such that AC = CD = DB. If $\angle B={28}^{\circ }$, then the measure of angle ACD is

1. ${54}^{\circ }$

2. ${64}^{\circ }$

3. ${72}^{\circ }$

4. ${84}^{\circ }$

Q. In the given figure, $\angle PQR={100}^{\circ }$, where P, Q and R are points on a circle with centre O. Find $\angle OPR$.

1. ${20}^{\circ }$
2. ${40}^{\circ }$
3. ${10}^{\circ }$
4. ${80}^{\circ }$

Q.

A chord of a circle which is twice as long as radius is the __ of the circle.

Q.

If A and B are two fixed points on the circumference of the circle such that line joining A and B passes through the centre of that circle, then the locus of the point P such that the $\angle APB={90}^{\circ }$ is ___ of the circle.

Q.

In the above figure O is the center of the circle. $\angle$AOB = ${80}^{\circ }$ ^, then complete the matching.

$\begin{array}{cc}Angle& Value\\ 1.ACB& a.90\\ 2.ADB& b.40\\ 3.ABC& c.80\\ 4.AOC& d.180\end{array}$

1. a-1, b-2, c-3, d-4

2. a-2, b-1, c-3, d-4

3. a-4, b-3, c-2, d-1

4. a-3, b-2, c-2, d-1

Q.

ABC is the right angled triangle with $\angle$ABC=${90}^{\circ }$, The centre of the circle passing through ABC lies on _______.

1. BC

2. a circle cannot be drawn through passing through A, B, C

3. AC

4. AB

Q.

In the given figure, AB = 5cm, BC = 4cm, AC = 3cm. Find the length of diameter of the circle.

1. 3 cm

2. 5 cm

3. 2.5 cm

4. 4 cm

Q.

In figure, A, B, and C are three points on a circle with centre O such that $\angle$BOC = ${30}^0$ and $\angle$AOB = ${60}^0$. If D is a point on the circle other than the arc ABC, find $\angle$ADC (in degrees).

__

Q.

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d units, find BP

1. √2d

2. √5d

3. 2√2d

4. d/√5

Q.

In the given figure if O is the centre of the circle, then $\angle CAB$ equals

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

2. ${50}^{\circ }$

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

4. ${75}^{\circ }$

Q.

If a circle is divided into 4 sectors, three of whose angles are ${75}^{\circ }$ , ${95}^{\circ }$ , and ${65}^{\circ }$ degrees. What is the angle of fourth sector?

1. 125 Degrees

2. 115 Degrees

3. 135 Degrees

4. 105 Degrees

Q.

In an equilateral $△$ABC inscribed in a circle, the perpendicular bisector of BC & the angle bisector of angles B & C meet at centre of the circle.

1. True
2. False

Q.

$O$ is the centre of the circle as shown in the figure, $\angle ORP=35°$ and the distance between $PandQ$ through $O$ is $4cm$. What is the measure of $\angle ROQ$ ?

1. $55°$

2. $35°$

3. $105°$

4. $70°$

Q. □ABCD is a cyclic quadrilateral. Answer the following questions:


(1) Name the arc intercepted by ∠D.
(2) If m∠B = 65°, what is the measure of m∠D?
(3) If m∠A = 125°, what is the measure of ∠C?
(4) What is angle inscribed in the arc BCD?

Q. If C1 and C2 are 2 circles with O and C as centres respectively and AB∥DE, then identify which angle is 50°.

1. 
2. 
3. 

Q.

Given a circle with O as the centre. Find the value of x.

1. 80°

2. 150°

3. 50°

4. 40°

Q.

Angle in a semicircle is

1. always an obtuse angle

2. either an acute angle or a right angle, but never an obtuse angle

3. always an acute angle

4. always a right angle

Q.

In the following figure if O is the centre of the circle, AC = 3 cm and BC = 4 cm, then the length of the diameter of the circle is

1. 4 cm

2. 3 cm

3. 5 cm

4. 12 cm

Q.

Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the midpoints of AB and CD respectively, prove that OMEN is a square. [4 MARKS]

Q.

Find the number of right angles turned through by the hour hand of a clock, when it goes from $12to6$.

Q. If R1 and R2 are two congruent circles with BD and CE as diameters , then find which angle is equal to 30°.

1. 
2. 
3. 
4.