Tangents from a Given Point

Q. The maximum number of tangents that can be drawn to a circle from a point outside it is ______.
[1 Mark]

Q. O is a point outside the circle and OA and OB are the two tangents drawn from the external point 'O'. If OA = 10cm, find the length of OB.

1. 10 cm
2. 8 cm
3. 5 cm
4. 20 cm

Q. How many tangents can be drawn to a circle from a point outside the circle?

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

Q.

The number of common tangents that can be drawn if two circles touch each other externally is

1. 2

2. 3

3. 4

4. 1

Q.

Tangents from an external point are

1. Equal

2. Unequal

3. Depends upon the radius of the circle

4. None of these

Q.

ABC is a right angled triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

1. 8 cm

2. 3 cm

3. 2 cm

4. 9 cm

Q.

In the given figure, two circles touch each other externally at point, P. AB is the direct common tangent of these circles. Select the statements that are true.

1. Tangent at point P bisects AB.

2. $\angle APB={40}^{\circ }$

3. $\angle APB={45}^{\circ }$

4. $\angle APB={10}^{\circ }$

Q.

In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is

1. 20 cm

2. $\frac{20}{3}cm$

3. 40 cm

4. $\frac{40}{3}cm$

Q.

In the figure; PA is a tangent to the circle. PBC is secant and AD bisects angle BAC. Select the statements that are true.

1. $\angle CAD=\frac{1}{3}(\angle PBA-\angle PAB)$

2. Triangle PAD is an isoscles triangle

3. $\angle CAD=\frac{1}{2}(\angle PBA-\angle PAB)$

4. $\angle CAD=\frac{1}{9}(\angle PBA-\angle PAB)$

Q.

In the given figure, R is an external point and RP and RQ are tangents drawn to the circle from R. $\angle POQis{90}^{\circ }$. The quadrilateral OPRQ is a ____and the $\angle$ POR is ___

1. $Kite,{60}^{\circ }$

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

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

4. $Square,{45}^{\circ }$