Length of Tangent

Q.

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

1. 10 cm

2. 25 cm

3. 15 cm

4. 20 cm

Q.

State 'T' for true and 'F' for false.
I. If one angle of a cyclic trapezium is four times the other, then the greater one measures ${144}^{\circ }$.
II. The length of the direct common tangent to two circles with radii R and r, having distance between the centres d, is $\sqrt{d^2-(R-r{)}^2}$

1. (I) F (II)F

2. (I) T (II)F

3. (I) T (II)T

4. (I) F (II)T

Q.

A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is

1. $\frac{1}{4}\times$ Area of ABCD

2. $\frac{1}{2}\times$ Area of ABCD

3. $\frac{1}{8}\times$ Area of ABCD

4. None of these

Q. A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. If AB=CD and AD=BC, then

Quadrilateral ABCD can be

1. rectangle
2. parallelogram
3. rhombus
4. square

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

1. Equal
2. Unequal
3. None of these
4. Depends upon the radius of the circle

Q.

The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.

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.

There are two circles each with radius 5 cm. The length of tangent AB is 26 cm. Find the length of tangent CD.

1. 16 cm

2. 15 cm

3. 21 cm

4. 24 cm

Q.

If the length of the tangent drawn at the point (1, 3) on the curve y = $3x^3$ is a, then find the value of $9a^2$

___

Q.

In the above figure, length of tangent is length of PT

1. True

2. False