Inscribed Angle Theorem

Q. Question 5
Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4m
Find the distance between the first and the last sapling.

Q. Two circles of same radii r and centres O and O touch each other at P as shown in Fig. 10.91. If O O is produced to meet the cirele C (O, r) at A and AT is a tangent to the circle C (O, r) such that OQ $\perp$ AT. Then AO : AO =

(a) 3/2

(b) 2

(c) 3

(d) 1/4

Q. The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is
(a) 8 cm
(b) $\sqrt{104}$ cm
(c) 12 cm
(d) $\sqrt{125}$ cm

Q.

A wheel has diameter $84cm$. Find how many complete revolutions must it take to cover $792meters$

Q. If the angle between 2 radii of a circle is 140°, then the angle between the tangents at the ends of the radii is?

Q. In Fig. 10.87 , BOA is a diameter of a circle and the tangent at a point P meets BA produced at T . If $\angle$PBO = 30⁰ , then find $\angle$PTA .

figure

Q. BC is chord of a circle with centre O. A is a point on major arc BC. Find the total measure of $\angle BAC$ and $\angle OBC$.

1. ${90}^{\circ }$
2. ${100}^{\circ }$
3. ${120}^{\circ }$
4. ${150}^{\circ }$

Q. Question 101 (i)

Find the scale.
Actual size 12 m, Drawing size 3 cm

Q.

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. $\angle$ADP = $\angle$BEQ = ${100}^{\circ }$. What is value of $\angle$PRD?

1. Can't be determined

2. ${60}^{\circ }$

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

4. ${20}^{\circ }$

Q. The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is

(a) $\sqrt{7}cm$

(b) 7 cm

(c) 5 cm

(d) 25 cm

Q.

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

1. 12 cm

2. 8.5 cm

3. √119 cm

4. 13 cm

Q. A tangent makes an angle of ___ with the radius of the circle at the point of contact.

1. 45 degrees
2. 90 degrees
3. 150 degrees
4. 180 degrees

Q. Consider the figure where $\angle AOB={90}^{\circ }$ and $\angle ABC={30}^{\circ }.$ Then, $\angle CAO$ = ___.

1. ${45}^{\circ }$
2. ${50}^{\circ }$
3. ${75}^{\circ }$
4. ${60}^{\circ }$

Q. Each wheel of a car is of diameter $80cm.$ How many complete revolutions does each wheel make in $10$ minutes when the car is travelling at a speed of $66$ $km/per$ hour?

Q. A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

Q.

Length of the tangent to a circle from a point 26 cm away from the centre is 24 cm. What is the radius of the circle?

1. 11 cm

2. 10 cm

3. 13 cm

4. 12 cm

Q.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $\angle$BOD = ${160}^{\circ }$, then find the measure of $\angle$BPD.

1. ${100}^{\circ }$

2. ${80}^{\circ }$

3. ${90}^{\circ }$

4. ${70}^{\circ }$

Q. In the given figure, O is the centre of the circle. A is any point on minor arc BC. Find the value of $\angle BAC-\angle OBC$.

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${120}^{\circ }$

Q.

In the given figure, LMN is the tangent to the circle with centre O. If $\angle$ PMN $={60}^{\circ }$, find $\angle$MOP.

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

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q. A tangent makes an angle of ___ with the radius of the circle at the point of contact.

1. 45 degrees
2. 90 degrees
3. 150 degrees
4. 180 degrees

Q.

ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle with centre O through A, B, C, D. If $\angle ADC={130}^{\circ }$, Calculate $\angle$BAC.

Q.
If $\angle BCD={50}^{\circ },$ then $\angle BAD$ = ___.

1. ${50}^{\circ }$
2. ${100}^{\circ }$
3. ${25}^{\circ }$
4. ${70}^{\circ }$

Q.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $\angle$BOD = ${160}^{\circ }$, then find the measure of $\angle$BPD.

1. ${100}^{\circ }$

2. ${80}^{\circ }$

3. ${90}^{\circ }$

4. ${70}^{\circ }$

Q. In the figure, 'O' is the centre of the circle. $\angle AOB={100}^o$ find $\angle ADB$.

Q.

In the adjoining figure 'O' is the center of circle, $\angle$CAO = ${25}^{\circ }$ and $\angle$CBO = ${35}^{\circ }$. What is the value of $\angle$AOB?

1. ${120}^{\circ }$

2. ${110}^{\circ }$

3. Data insufficient

4. ${55}^{\circ }$

Q. If PA and PB are tangents to the circle with centre O such that $\angle$APB = 50⁰, then $\angle$OAB is equal to

(a) 25⁰ (b) 30⁰ (c) 40⁰ (d) 50⁰

Q. Question 10
In the figure, if $\angle AOB={90}^{\circ }and\angle ABC={30}^{\circ },then\angle CAO$ is equal to

(A) ${30}^{\circ }$
(B) ${45}^{\circ }$
(C) ${90}^{\circ }$
(D) ${60}^{\circ }$

Q. In the given figure, RQ is a tangent to the circle with centre O. If SQ = 6 cm and QR = 4 cm, then OR is equal to [CBSE 2014]
(a) 2.5 cm
(b) 3 cm
(c) 5 cm
(d) 8 cm

Q. Find the length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre of the circle.

Q. The angle between two radii of a circle is 95°, then find the angle between the tangents at the end of the radii?