Circle and Line in a Plane

Q.

If two circles are equal, then their radii are equal. True or False?

1. True

2. False

Q. If O is the center of the circle, then the value of $\theta$ in the adjoining figure is

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${75}^{\circ }$

Q. The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm. The length of the chord MN is .

1. 15 cm
2. 17 cm
3. 18 cm
4. 20 cm

Q. Number of circles that can be drawn through three non-collinear points is

(a) 1

(b) 0

(c) 2

(d) 3

Q.

Circles having the same centre and different radii are called

1. Concentric circles

2. Semi-circles

3. Equal circles

4. Congruent circles

Q. How draw a regular hexagon ?

Q. Assertion (A) In the given figure, If O is the centre of the circle and AC is the diameter with $\angle APB={120}^{\circ }$, then $\angle BQC={150}^{\circ }$.

Reason (R) In a cyclic quadrilateral, the sum of opposite angles is ${180}^{\circ }$.
which of the following is true?

1. (A) is true and (R) is the correct explanation of (A)
2. (A) is false and (R) is the correct explanation of (A)
3. (A) is true and (R) is false
4. Both (A) and (R) are false

Q. How to draw a circle with three non collinear points?

Q.

What is the circumference of a circle with radius 2r units?

1. 2$\pi$r

2. $\pi r^2$

3. 4$\pi r$

4. $\pi$r

Q.

In a circle of radius 5 cm, $AB$ and $AC$ are two chords such that $AB=AC=6cm.$ Find the length of the chord $BC$.

Q.

Circles with the same centre and different radii are called __ circles.

Q. Match the unknown angle $x$ in each case if O is the centre of each circle.

1. ${40}^{\circ }$
2. ${30}^{\circ }$
3. ${90}^{\circ }$

Q. Question 8
ABCD is cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and $\angle ADC={140}^{\circ },then\angle BAC$ is equal to

(A) ${80}^{\circ }$
(B) ${50}^{\circ }$
(C) ${40}^{\circ }$
(D) ${30}^{\circ }$

Q. In the following figure QT$\perp$PR and QS$=$PS. If $\angle$TQR$={40}^o$ and $\angle$RPS$={20}^o$ then value of x is?

1. ${80}^o$
2. ${25}^o$
3. ${15}^o$
4. ${35}^o$

Q. The lengths of the two tangents from an external point to a circle are .....

1. equal
2. different
3. none of the above
4. both A and B

Q. Match the unknown angle $x$ in each case if O is the centre of each circle.

1. ${40}^{\circ }$
2. ${30}^{\circ }$
3. ${90}^{\circ }$

Q. Give a method to find the centre of a given circle.

Q. In the given figure, tangents PQ and PR are down to a circle such that angle $RPQ={30}^0$. A chord RS is drawn parallel to the tangent PQ. Find the angle RQS.

Q. The diagonals of quadrilateral ABCD intersect at O, prove that $\frac{ar\left(△ACB\right)}{ar\left(△ACD\right)}=\frac{BO}{DO}$

Q.

Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?

1. The number of intersection points between PQ and circle changes from
   $0\to 1\to 2\to 1\to 0.$

2. The number of intersection points between PQ and circle changes from
   $0\to 1\to 2\to 0.$

3. The number of intersection points between PQ and circle changes from
   $0\to 1\to 0.$

4. The number of intersection points between PQ and circle changes from
   $0\to 1\to 2.$

Q. In the diagram at the right the segments shown are tangent to the circle Find the value of x

1. 5
2. 6
3. 7
4. 9

Q. $△PQR$ is inscribed in a semicircle. $PQ=PR=7$ cm.
(i) What is the measure of $\angle QPR?$
(ii) Find the area of the shaded region.

Q. PQRS is a isosceles trapezium with $PQ\parallel RS$ , if P $=60$, then Q equals to

1. $30$
2. $60$
3. $120$
4. $150$