Terms Related to Circles

Q.

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Q. In the given figure, the two concentric circles are centred at O. If BD = 2 cm, CD = 12 cm, then the radius of the larger circle is

1. 
   6 cm
2. 
   8 cm
3. 
   10 cm
4. 
   12 cm

Q. How many tangents can be drawn parallel to the given tangent?

1. 0
2. 2
3. Infinite
4. 1

Q. Under which condition can a secant to a circle be called a tangent?

1. The secant is a curved line.
2. The points of intersection are infinite distance apart.
3. The secant passes through the centre of the circle.
4. The points of intersection are coincident.

Q.

A radius of a circle is a line segment with one end point at _______________ and the other end-point on ______________ .

Q.

Two parallel chords are drawn on either side of the centre of a circle of diameter 30 cm. If the length of one chord is 24 cm and the distance between the two chords is 21 cm, then find the length of another chord.

1. 10 cm

2. 17 cm

3. 18 cm

4. 8 cm

Q.

The line segment joining any two points on a circle and passing through the center of the circle is called the _____ of the circle.

Q. is a line that touches the circle only at one point and is a line that cuts the circle at two distinct points.

1. Tangent
2. Chord
3. Diameter
4. Secant
5. Radius

Q. The circumference of a circular garden is 572 m.Outside the garden a road, 3.5 m wide runs around it.Calculate the cost of repairing the road at the rate of Rs. 375 per 100 sq. m.

Q. $\text{In the given figure, PT is a tangent drawn}\text{from an external point T to the circle with}\text{centre O and PQ is the diameter of the}\text{circle. Point Q and T are joined by a line}\text{which is intersecting the circle at R. If}\angle POR={78}^{\circ },\text{then find}\angle PTR.$

1. ${39}^{\circ }$
2. ${51}^{\circ }$
3. ${61}^{\circ }$
4. ${41}^{\circ }$

Q.

Question 5
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Q. A wheel starts moving in such a way that point A comes from bottom to top as shown.The distance travelled by the wheel is equal to one half of the circumference.

1. True
2. False

Q. In the given figure, the two concentric circles are centred at O. If BD = 2 cm, CD = 12 cm, then the radius of the larger circle is

1. 
   6 cm
2. 
   8 cm
3. 
   10 cm
4. 
   12 cm

Q. A, B, C are any points on the circle with centre O. m(arc BC)=120${}^{\circ }$ and m(arc AB)=130${}^{\circ }.$
Then, find the value of m(arc ABC) .

Q. $\text{In the given figure, PT is a tangent drawn}\text{from an external point T to the circle with}\text{centre O and PQ is the diameter of the}\text{circle. Point Q and T are joined by a line}\text{which is intersecting the circle at R. If}\angle POR={78}^{\circ },\text{then find}\angle PTR.$

1. ${39}^{\circ }$
2. ${51}^{\circ }$
3. ${61}^{\circ }$
4. ${41}^{\circ }$

Q.

Question 5
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Q. Two parallel chords are drawn on either side of the centre of a circle of diameter 30 cm. If the length of one chord is 24 cm and the distance between the two chords is 21 cm, then find the length of another chord.

Q. Question 10
In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and $\angle BQR={70}^{\circ }$ , then $\angle$AQB is equal to
(A) 20°
(B) 40°
(C) 35°
(D) 45°

Q. How many tangents can we draw to a given circle?

1. 0
2. 1
3. 2
4. Infinite

Q. When a circle and a line are in a plane, they may have ____ point/points of intersection.

1. zero
2. infinite
3. one
4. two

Q. The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm & 34 cm, Find the distance between their centres .

Q. The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm & 34 cm, then find the distance between their centres.

Q. A, B, C are any points on the circle with centre O. m(arc BC)=120${}^{\circ }$ and m(arc AB)=130${}^{\circ }.$
Then, find m(arc ABC), m (arc ACB), and m (arc BAC).
[3Marks ]

Q. In the given figure, ABCD is a rectangle, OB is the radius, PB is the tangent at point B and $\angle OBC={30}^{\circ }$. Then, the value of x is___.

1. ${90}^{\circ }$
2. ${30}^{\circ }$
3. ${110}^{\circ }$
4. ${60}^{\circ }$

Q. A tractor wheel covers a distance of 9.42 m on its 1 complete rotation. Then the radius of the wheel is . Take $\pi =3.14$

1. $3m$
2. $1.5m$
3. $6m$

Q. ______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

1. Tangent, secant
2. Secant, secant
3. Secant, tangent
4. Tangent, tangent

Q. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, then what is the radius of the circle?

Q. $\text{In the given figure, PT is a tangent drawn}\text{from an external point T to the circle with}\text{centre O and PQ is the diameter of the}\text{circle. Point Q and T are joined by a line}\text{which is intersecting the circle at R. If}\angle POR={78}^{\circ },\text{then find the value of}\angle PTR.$

Q. A wheel starts moving in such a way that point A comes from bottom to top as shown. The distance travelled by the wheel is its circumference.

1. equal to
2. half of
3. twice

Q. How many tangents can a circle have?