Tangent perpendicular to radius at point of contact

Q.

Two circles touch each other internally at a single point. Their radii are 2 cm and 3 cm. The biggest chord of outer circle which is a tangent to the inner circle, is of length ____.

1. 2$\sqrt{2}$ cm

2. 3$\sqrt{2}$ cm

3. 2$\sqrt{3}$ cm

4. 4$\sqrt{2}$cm

Q.

A tangent PQ at a point P on a circle of radius 5 cm meets a line through the center O at a point Q such that OQ =13 cm. Find the length of PQ.

1. 12 cm

2. 13 cm

3. $\sqrt{119}$

4. 8.5 cm

Q.

A point A is 17 cm away from the center of the circle and the length of tangent drawn from A to the circle is 15 cm. Find the radius of the circle.

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Q.

From a point P, two tangents PA and PB are drawn to a circle with center O as shown. If ∠ AOB = 120°, then find the value of ∠ APB.

Q.

There are two concentric circles, each with center O and of radii 10 cm and 26 cm respectively. Find the length of the chord AB of the outer circle which touches the inner circle at P.

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Q. In fig., a circle with centre $O$ is inscribed in a quadrilateral $ABCD$ such that, it touches the sides $BC,AB,AD$ and $CD$ at points $P,Q,R$ and $S$ respectively, If $AB=29$ cm, $AD=23$ cm, $\angle B={90}^o$ and $DS=5$ cm, then the radius of the circle (in cm) is:

1. $11$
2. $18$
3. $6$
4. $15$

Q.

Find the length of the tangent drawn to a circle of radius 8 cm, from a point which is at a distance of 10 cm from the center of the circle.

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Q. A tangent $AB$ at a point $A$ of a circle of radius $5$ cm. meets a line through the centre $O$ at a point $B$, so that $OB$ $=$ $12$ cm. Then find the length of $AB$.

1. $\sqrt{119}$ cm
2. $119$ cm
3. $\sqrt{126}$ cm
4. $112$ cm

Q. The in-radius of an equilateral triangle is of length $3$ cm, then the length of each of its median is:

1. $12$ cm
2. $\frac{9}{2}$
3. $9$ cm
4. $4$ cm

Q.

AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.

1. 10 cm

2. 8 cm

3. 15 cm

4. 13 cm

Q.

The length of the tangent to a circle from a point outside the circle measures 12 cm. The distance of the point from the centre is 15 cm.
Find the radius of the circle.

1. 10cm

2. 8cm

3. 12cm

4. 9cm

Q.

$\text{If AB is the tangent to the circle with}\text{center O then, find the measure of}\angle OCP.$
$\text{Given that OP = PC.}$

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

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

3. ${15}^{\circ }$

4. ${60}^{\circ }$

Q.

From a point P, two tangents PA and PB are drawn to a circle with center O as shown.
If angle AOB = ${100}^{\circ }$, then find the value of $\angle APB.$

1. ${40}^{\circ }$

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

3. ${80}^{\circ }$

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

Q. Tangent to a circle makes an angle of ${45}^{\circ }$ with the radius at the point of contact.

1. False
2. True

Q. The radius of a circle and the tangent are perpendicular at the point of ___ .

Q.

The length of the tangent from a point A to a circle, of radius 3 cm, is 4 cm. Find the distance of A from the center of the circle.

1. $\sqrt{7}$ cm

2. 7 cm

3. 5 cm

4. 25 cm

Q. The distance between any two parallel tangents is equal to the ___of the circle.

1. radius
2. diameter
3. circumference
4. semi circumference