Diameter Subtends Right Angle at the Circumference

Q.

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

1. ${30}^{\circ }$

2. ${45}^{\circ }$

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

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

Q. If AC = 4 cm and BC = 3 cm, then the diameter of the circle is equal to .

1. 6 cm
2. 5 cm
3. 4 cm
4. 3 cm

Q.

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

1. $\sqrt{2}d$ units

2. $\frac{d}{\sqrt{5}}$ units

3. $\sqrt{5}d$ units

4. $2\sqrt{2}d$ units

Q.

In the given circle, with AB as diameter, find the value of 'x'.

1. ${50}^{\circ }$

2. ${40}^{\circ }$

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

4. ${30}^{\circ }$

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. 5 cm

2. 12 cm

3. 4 cm

4. 3 cm

Q.

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

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

2. ${75}^{\circ }$

3. ${50}^{\circ }$

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

Q.

Assertion: Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.

Reason: Angle in a semi-circle is a right angle.

Which of the following options is correct?

1. Both assertion and reason are true and reason is the correct explanation of assertion.

2. Both assertion and reason are true, but reason is not the correct explanation of assertion.

3. Assertion is true, but the reason is false.

4. Assertion is false, but the reason is true.

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. 6.5 cm

2. 7.5 cm

3. 12 cm

4. 13 cm

Q.

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

1. 3 cm

2. 2.5 cm

3. 5 cm

4. 4 cm

Q.

The angle subtended by the diameter at the circumference is

1. an acute angle.

2. an obtuse angle.

3. a right angle.

4. an acute angle or a right angle, but never an obtuse angle.