Tangent Perpendicular to Radius at Point of Contact

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. Question 1
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle, . Find the radius of the inner circle.

Q.

State true or false.
The length of the tangent drawn from a point 10 cm away from the center of a circle of radius 6 cm is 8 cm.

1. √7 cm

2. 2√7 cm

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 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. The line l is tangent to the circle S at the point A; B and C are points on i on opposite sides of A and the other tangents from B, C to S intersect at a point P. If B, C vary along i in such a way that the product of AB.AC is constant, find the locus of P.

Q.

A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is

___ cm.

Q. 54. Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB=2CD . Let AD be perpendicular to AD and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is (A) 3 (B) 2 (C) 3/2 (D)1

Q. PQ is a chord of circle The tangent XR at X on the circle cuts PQ produced at R If XR = 12 cm, PQ = x cm, QR = x - 2 cm then x in cm is

1. 6
2. 10
3. 7
4. 14

Q. Two circle touch each other externally at $C$ and $AB$ is a common tangent to the circles. Then, $\angle ACB=$

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q.

The length of a tangent from a point Q to a circle is 24 cm. The distance between Q and the center of the circle is 25 cm. The radius of the circle is _____ cm.

Q. A tangent is drawn to a circle from a point $P$ which is at a distance of $13$ cm from the center of the circle of radius $5cm.$ The length of the tangent is?

1. $10cm$
2. None of the options
3. $12cm$
4. $18cm$

Q.

In a triangle ABC, O is the center of incircle PQR, $\angle$BAC = ${65}^{\circ }$, $\angle$BCA = ${75}^{\circ }$, find $\angle$ ROQ.

1. ${140}^{\circ }$

2. ${120}^{\circ }$

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

4. Can't be determined

Q. If the given figure, $l$ & $m$ are two parallel tangents to a circle with centre $O$, touching the circle at $A$ and $B$ respectively. Another tengent at $C$ intersects the lone $l$ and $D$ and lone $m$ at $E$. Find $\angle DOE$

Q.

A circle is inscribed in a triangle with sides 3, 4 and 5 cm. The radius of the circle is

___ cm.

Q.

The radius is ___ the tangent at the point of contact.

1. parallel to

2. at an acute angle with

3. perpendicular to
4. not perpendicular to

Q. Use the figure alongside to fill in the blank:​
(iii) Tangent to the circle is

Q.

The radius of a circle and the tangent at the __ are perpendicular.

Q. AB and CD are two common tangents to circles which touch each other at C. If D lies on AB such that CD = 4 cm, then AB is equal to

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

Q. A tangent to a circle touches it at ....... point (s).

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 of PQ is :

1. $\sqrt{113}$ cm
2. $\sqrt{112}$ cm
3. $\sqrt{85}$ cm
4. $\sqrt{119}$ cm

Q. In the given diagram, if $l$ and $m$ are two tangents and $AB$ is a chord making an angle of ${60}^0$ with the tangent $l$, then the angle between $l$ and $m$ is

1. ${45}^0$
2. ${60}^0$
3. ${30}^0$
4. ${90}^0$

Q. In the following figure, point 'A' is the centre of the circle. Line MN is tangent at point M. If AN$=10$cm and MN$=5$cm, determine radius of the circle.

Q. If the length of the common chord of two intersecting equal circles be 6 cm and if the radius of each circle be 5 cm then the distance between the centers of the circle is

1. 7 cm
2. none
3. 8 cm
4. 9 cm

Q.

A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x is ___ cm.

Q. From a point A which is at a distance of 10 cm from the center O of a circle of radius 6 cm, the pair of tangents AB and AC to the circle are drawn. Then the area of Quadrilateral ABOC is:

1. $24c{m}^2$
2. $48c{m}^2$
3. $96c{m}^2$
4. $100c{m}^2$