Tangent

Q.

What is the maximum number of common tangents that can be drawn to two circles of different radii, touching each other internally?

1. $1$

2. $4$

3. $3$

4. $2$

Q. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Q. 15. What is the maximum number of parallel tangent a circle can have on a diameter

Q.

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.

1. 5cm

2. 6cm

3. 10cm

4. 7cm

Q.

In the figure, PB and QA are perpendicular to segment AB. If OA = 5 cm, PO = 7cm and area ($\Delta$QOA) = 150 $c{m}^2$, find the area of $\Delta$POB.

1. $233c{m}^2$

2. $294c{m}^2$

3. $300c{m}^2$

4. $420c{m}^2$

Q. What is the shortest distance from the tangent to the centre of the circle?

1. Radius
2. > radius
3. < radius
4. Can't say

Q. Question 4
Draw a circle and two parallel lines such that one is a tangent and the other, a secant to the circle.

Q.

Two concentric circles are of radii $5cm$ and $3cm$.

Find the length of the chord of the larger circle (in $cm$) which touches the smaller circle.

Q. Question 3
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 PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) $\sqrt{119}cm$

Q.

How many circles can pass through 3 given points not in a straight line?

1. 1

2. 0

3. 3

4. 2

Q.

State true or false.
Maximum number of tangents parallel to a given secant of a circle are four.

1. 1

2. 2

Q.

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

1. $1$

2. $2$

3. $3$

4. $4$

Q. P and Q are the centres of two circles whose radii are 5 cm and 11 cm, respectively. If the direct common tangent to the circles meets PQ at M, then, M divides PQ in the ratio

1. 5 : 11 internally
2. 11 : 5 internally
3. 5 : 11 externally
4. 11 : 5 externally

Q.

A tangent cuts a circle at more than one point.

1. True

2. False

Q. Draw a cirlce and two lines parallel to a given line such that one is a tangent and the other is a secant to the circle.

Q. Two equal chords, $AB$ and $CD$ are at a distance of 10 cm from each other. The distance of chord $AB$ from the centre .

1. $6cm$
2. $5cm$
3. $8cm$

Q. There is one and only one circle passing through three given___ points

1. Nearest
2. Collinear
3. Non-collinear
4. Far-off

Q. Find the locus of the centres of the circles which touch a given line at a given point.

Q.

P is any point inside the circle. A line AB is shifted right to pass through P. Then, what is the line called?

1. Diameter

2. Tangent

3. Secant

4. Chord

Q. Question 3
The length of tangents from an external point P on a circle with centre O is always less than OP.

Q.

A tangent at a point $A$ on the circle meets a line through the centre of the circle at a point $B$ so that $OB=13cm$ and $AB=12cm$. Find the radius of the circle.

1. $3cm$

2. $5cm$

3. $7cm$

4. $10cm$

Q. What is the shortest distance from the tangent to the centre of the circle?

1. Radius
2. > radius
3. < radius
4. Can't say

Q.

Question 4
If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

Q.

A circle of diameter 13 cm has two chords of lenght 12cm and 5cm. If both the chords lie on the same semicircle, what is the distance between the chords?

1. 3.5 cm

2. 2.5 cm

3. 2 cm

4. 1.5 cm

Q. Prove that circles with equal radius are congruent.

Q.

The set of values of 'c' so that the equations $y=\left|x\right|+cand{x}^2+y^2-8\left|x\right|-9=0$ have no solution is

1. $(\infty ,-3)\cup (3,\infty )$
   

2. $(-3,3)$
   

3. $(-\infty ,5\sqrt{2})\cup \left(5\sqrt{(}2\right),\infty )$
   

4. $5\sqrt{2}-4,\infty$

Q.

Any line segment which touches a circle at exactly one point is called the __ to the circle at that point.

Q. How many diameter are there? Name all the diameter in a circle?

Q. The maximum number of circles that can pass through 3 non-collinear points is 1.

1. True
2. False

Q. 47. If angle between two tangents PT and PQ from a point T to a circle of radius r and centre O is 60^° , then prove that PT =\sqrt{}3r