Angle in a Semi Circle Is Right Angle

Q.

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter.

The sum of the areas of shaded part is ______

1. equal to the area of semi-circle with diameter BC

2. equal to the area of $\Delta$ABC

3. equal to half of the area of $\Delta$ABC

4. equal to twice the area of $\Delta$ABC

Q.

O is the centre of the circle. AD and BC are perpendicular to XY. CB cuts the circle at E, then which of the options are correct?

1. BE=AD

2. CD=CE

3. BD=BE

4. AD=CE

Q.

Construct the quadrilateral ABCD in which AB = 7cm, BC = 9 cm and $\angle$ ABC = ${135}^0$, given that AC is its only line of symmetry. Name the geometrical name of the quadrilateral.

1. Trapezium

2. Rhombus

3. None of these

4. Kite

Q. What is the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is ${60}^{\circ }$

1. $(\frac{308}{3}-49\sqrt{3})c{m}^2$
2. $(\frac{320}{3}-50\sqrt{3})c{m}^2$
3. $49c{m}^2$
4. $\frac{308}{3}c{m}^2$

Q.

A circle having radius 4 cm contains a chord of length 4 cm and subtends an angle of 60 degrees. Find the area of the minor segment of the chord.

1. 2

2. 1.5

3. 3

4. None of these

Q. ABCD is a parallelogram. If the radius of the circle passing through all the vertices of the parallelogram is 4 cm, then find length of AC.

Q.

A triangle is drawn by joining a point on the semi-circle to the ends of the diameter. Two semi-circles are drawn with the other two sides as diameter.

Find the sum of the areas of shaded part.

Q.

Two circles intersect at points A and B.The points P and Q are the other ends of the diameter through A

Then P, B, Q_________

1. are vertices of a triangle

2. lies inside the circle

3. lies on a straight line

4. None of these

Q.

In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that $\angle PQR={58}^{\circ },$ calculate $\angle RPQ.$

1. $\angle RPQ={62}^{\circ }$

2. $\angle RPQ={39}^{\circ }$

3. $\angle RPQ={82}^{\circ }$

4. $\angle RPQ={32}^{\circ }$

Q.

A circle having radius 4 cm contains a chord of length 4 cm and subtends an angle of 60 degrees. Find the area of the minor segment of the chord.

1. $2c{m}^2$

2. $1.5c{m}^2$

3. $3c{m}^2$

4. $0.5c{m}^2$

Q.

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

1. 3 cm

2. 2.5 cm

3. 5 cm

4. 4 cm

Q.

​
In the given figure, AB = 5 cm, BC = 4 cm, AC = 3 cm. The diameter of the circle is

1. 3 cm

2. 5 cm

3. 4 cm

4. 2.5 cm

Q.

If one angle of a cyclic quadrilateral measures 60 degrees, then the angle opposite to it measures

1. 60 degrees

2. 100 degrees

3. 90 degrees

4. 120 degrees

Q.

ABCD is a parallelogram. If the radius of the circle passing through all the vertices of a parallelogram is 4 cm, then the length of the diagonal AC is ___.

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.

What is the angle subtended by the diameter AB at the circumference of the circle?

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

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

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

4. Data inadequate