Lengths of tangents drawn from external point

Q.

In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle . Find TQ : TR.

1. 8 : 7

2. 1 : 1

3. 7 : 8

4. 5 : 4

Q.

2 tangents are drawn from a point P to a circle shown . If PA = 8 cm, what is the value of PB

1. 18 cm

2. 16 cm

3. 8 cm

4. 4 cm

Q.

In figure, a circle touches the side BC of $△$ABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter (in cm) of $△$ABC.

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Q. E is a point outside the circle as shown. ME and NE are tangents drawn to the circle from this point. Quadrilateral OMEN is symmetrical with respect to OE.

1. True
2. False

Q. Two tangents are drawn to a circle from an external point $A$, touching the circle at the points $P$ and $Q$. A third tangent intersects segment $AP$ at $B$ and segment $AQ$ at $C$ and touches the circle at $R$. If $AQ=10$ units, then the perimeter of $\Delta ABC$ is

1. $20.0$
2. $40.0$
3. $22.0$
4. $20.5$

Q.

In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quad. ABCD.

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Q. In the figure, $PA$ and $PB$ are tangents to the circle drawn from an external point $P$. Also $CD$ is a tangent to the circle at $Q$.
If $PA=8cm$ and $CQ=3cm$, then $PC$ is equal to:

1. $11cm$
2. $5cm$
3. $24cm$
4. $38cm$

Q. Okay, now this guy is stuck. You need to help him out. What is the first thing to identify?

1. Lengths of tangents drawn from an external point are equal.
2. Radius is perpendicular to the tangent at the point of contact.
3. The length of radius is same at any point on the circumference of the circle.
4. The line joining the external point and the centre of the circle bisects the angle between the tangents.

Q.

In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?

1. 3AE = AB + BC + AC

2. AC + AB = BC

3. AB + BC + AC = 4AE

4. 2AE = AB + BC + AC

Q.

Tangents from a point P are drawn onto a circle with angle between them as ${120}^{\circ }$ . The tangents from P meet the circle at A and B. If a line is drawn from point P through the center of the circle O, then find the measure of $\angle$POA.

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

2. ${25}^{\circ }$

3. ${45}^{\circ }$

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

Q. In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?

1. 25 cm
2. 26 cm
3. 27 cm
4. 24 cm

Q.

From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. Points O and P are joined. The ratio of angles OPR and OPQ is

1. 1:1

2. 2:1

3. 3:1

4. 4:1

Q.

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then

1. $AD=AB+BC+CA$

2. $2AD=AB+BC+CA$

3. $4AD=AB+BC+CA$

4. $3AD=AB+BC+CA$

Q.

The lengths of tangents drawn from an external point to a circle are equal.

1. False

2. True

Q.

In the given figure, PQ and PR are two tangents drawn from an external point P to a circle with centre 'O'. If OQ = 3 cm and PS = 2cm then, find the perimeter (in cm) of quadrilateral PQOR.

1. 12
2. 14
3. 10
4. 16

Q.

If a quadrilateral ABCD is drawn to circumscribe a circle, then which of the options is true?

1. AC + AD = BD + CD

2. AB + CD = BC + AD

3. AB + CD = AC + BC

4. AC + AD = BC + DB