Angle in a Semicircle

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.

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.

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.

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

1. 90º

2. 45º

3. Data inadequate

4. 60⁰

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

1. ${45}^{\circ }$

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

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

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

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 following figure, if O is the centre of the circle then $\angle DOE$ equals

1. ${45}^{\circ }$

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

3. ${75}^{\circ }$

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

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.

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. ${84}^{\circ }$