Converse of Tangent Theorem

Q.

The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is

1. 4 cm

2. 6 cm

3. 8 cm

4. 10 cm

Q.

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

1. 2 $\sqrt{313}$

2. 10

3. 7

4. 12

Q. Let $ABCD$ be a unit square. Draw a quadrant of a circle with $A$ as centre and $B,D$ as endpoints of the arc. Similarly, draw a quadrant of a circle with $B$ as centre and $A,C$ as endpoints of the arc. Inscribe a circle $\Gamma$ touching the arcs $AC$ and $BD$ both externally and also touching the side $CD.$ Find the radius of the circle $\Gamma$.

1. $\frac{1}{4}$
2. $\frac{1}{8}$
3. $\frac{1}{2}$
4. $\frac{1}{16}$

Q.

The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is

1. 4 cm

2. 6 cm

3. 8 cm

4. 10 cm

Q.

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

Q. In figure, from an external point $P$, a tangent $PT$ and a line segment $PAB$ is drawn to a circle with centre $O$.$ON$ is perpendicular on the chord $AB$.
Prove that:-

Q. $\text{In the given figure, PT is a tangent of a}\text{circle, with centre O, at point R. If}\text{diameter SQ is produced, it meets with}\text{PT at point P with}\angle SPR=x\text{and}\angle QSR=y,\text{then find the value of}x+2y\text{(in degrees)}.$

1. 90

Q. Let a circle be given by $2x(x-a)+y(2y-b)=0(a\ne 0,b\ne 0)$. If two chords, each bisected by the x-axis, can be drawn to the circle from $(a,\frac{b}{2})$, then

1. $a^2>2b^2$
2. $a^2>b^2$
3. $a^2<b^2$
4. $a^2<2b^2$

Q. Construct a chord of length $5cm$ in a circle of radius $3cm$. Construct tangents at the ends of the chord.

Q. A line perpendicular to a radius at its point on the circle necessarily not be a tangent to the circle.

1. True
2. False

Q. Let $ABC$ be a right triangle in which $AB=3cm,BC=4cm$ and $\angle B={90}^o.$ $BD$ is the perpendicular from $B$ on $AC.$ The circle through $B,C,D$ is drawn. Construct the tangents from $A$ to this circle.

Q.

A point A is 26 cm away from the center of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.

1. 10

2. 2 $\sqrt{313}$

3. 12

4. 7