Lengths of Tangents Drawn from External Point

Q.

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then

1. $AD=AB+BC+CA$

2. $3AD=AB+BC+CA$

3. $4AD=AB+BC+CA$

4. $2AD=AB+BC+CA$

Q.

In fig., CP and CQ are tangents to a circle with center O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length (in cm) of BR

__

Q.

In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quad. ABCD.

__

Q.

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

1. 6 cm

2. 16 cm

3. 10 cm

4. 8 cm

Q.

In the given figure, quadrilateral ABCD is circumscribed and AD $\perp$ AB. If the radius of incircle is 10 cm, find the value of x.

__

Q.

In the given figure, $△$ABC is circumscribed. The circle touches the sides AB, BC and CA at P, Q, R respectively. If AP = 5 cm, BP = 7 cm, AC = 14 cm and BC = $x$ cm, find the value of $x$.

__

Q.

A triangle ABC is drawn to circumscribe a circle such that the segments BS and SC are of lengths 6 cm and 8 cm respectively. If the length of the segment AT is x cm , then find the perimeter of the triangle.

1. 12+x

2. 14+x

3. 24+2x

4. 28+2x

Q.

In figure, a circle touches the side BC of $△$ABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter (in cm) of $△$ABC.

__

Q.

Prove that the parallelogram circumscribing a circle, is a rhombus.

Q.

If tangents PA and PB from a point P to a circle with center O are inclined to each other at an angle of ${80}^{\circ }$ then find the measure of $\angle POA$

1. ${70}^{\circ }$

2. ${50}^{\circ }$

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

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

Q. If $D$ and $E$ are the mi-points of the sides $AB$ and $AC$, respectively of the $△ABC$ what percent of the whole triangular region is the area of the trapezium $BCED$?

1. $50$%
2. $25$%
3. $75$%
4. $60$%

Q.

ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with center O is inscribed in $△$ABC. Find the radius of the circle.

1. 3 cm

2. 1 cm

3. 2 cm

4. 4 cm

Q. In the below figure, BC= ___.

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

Q. If two circles touch each other externally then the number of common tangents to the circles is

1. $4$
2. $3$
3. $2$
4. $1$

Q.

State True or False.

In the given figure, common tangents AB and CD to the two circles with centre O1 and O2 intersect at E. Then AB = CD .

Q. What would you read this question as?

1. A quadrilateral with unequal lengths.
2. 4 points and tangents to the circle from those points.
3. A quadrilateral with a pair of parallel sides.
4. A random shape.

Q. If the circle $C_1:x^2+y^2=16$ intersects another circle $C_2$ of radius 5 in such a manner that the common chord of maximum length $8$ has a slope equal to $\frac{3}{4}$, then coordinates of centre of $C_2$ are -

1. $(\frac{9}{5},-\frac{12}{5})$
2. $(\frac{9}{5},\frac{12}{5})$
3. $(-\frac{9}{5},-\frac{12}{5})$
4. $(-\frac{9}{5},\frac{12}{5})$

Q.

In the given diagram , $△$ PQO is congruent to which triangle ?

__

Q.

$△$ABC is a right- angled triangle with AB = 12 cm and AC = 13 cm. A circle with center O has been inscribed inside the triangle. Calculate the radius of the inscribed circle.

__

Q. In the figure, quadrilateral ABCD is circumscribed, find the value of x.

Q.

Which of the following statements fits best as per the diagram given below.

1. PA = PD

2. PA = AQ

3. BQ = DS

4. RC = DS

Q. A circle touches all side of a parallelogram so that parallelogram must be-

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

Q. $TP$ and $TQ$ are tangents from $T$ to the circle with centre $O.$ Then is it possible to draw a circle through the points $P,O,Q$and $T?$

1. No
2. Yes
3. Cannot say
4. Data insufficient

Q.

2 tangents are drawn from a point P to a circle as shown . If PA : AB = 5:2 and the perimeter of triangle APB is 48 cm, the length of PB is:

__

Q. In the adjoining figure, O is the centre of the circle. Determine $\angle$ACB, if PA and PB are tangents and $\angle$APB$={60}^o$.

Q.

In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC =x cm, CR = 4 cm and AS = 6 cm, the value of x is

___ cm.

Q. In the given figure if $AB||DC$ find the value of $x$. If $OA=3x-1$ $PB=2x+1$ $OC=5x-3$ and $OD=6x-5$

Q. In the given figure, $RST$ is the tangent to the circle with centre $O$, at $S.$ $AOS$ is a straight line $BO\parallel RT$ and $\angle ORS={46}^{\circ }.$ Then $\angle BAC$ equals

1. ${22}^{\circ }$
2. ${46}^{\circ }$
3. ${23}^{\circ }$
4. ${32}^{\circ }$

Q.

ABC is a right angled triangle, right angled at B with AB = 3 cm and BC = 4 cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.

__