Tangent Secant Segments Theorem

Q.

Two circles of radii 25cm and 9cm touch each other externally. Find the length of the direct common tangent. [4 MARKS]

Q. In the given figure PA = 4 cm and PB = 9 cm, the value of PT is equal to

1. 5 cm
2. 6 cm
3. 4 cm
4. 7 cm

Q.

The lengths of tangents drawn from an external point are equal.

1. True

2. False

Q. In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1cm, then PS = ______cm.

1. 7
2. 10
3. 49
4. 4.9

Q. In the given figure PA = 3 cm and PB = 6 cm, the value of PT is equal to

1. $2\sqrt{2}cm$
2. $3\sqrt{3}cm$
3. $2\sqrt{3}cm$
4. $3\sqrt{2}cm$

Q. In the given figure PA = 2 cm and PB = 8 cm, the value of PT is equal to

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

Q. In the given figure PA = 3 cm and PT = 4 cm, the value of PB is equal to

1. $\frac{8}{3}$ cm
2. $\frac{16}{9}$ cm
3. $\frac{4}{9}$ cm
4. $\frac{16}{3}$ cm

Q.

In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

Q. In the given figure PA = 2 cm and PB = 8 cm, the value of PT is equal to

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

Q. In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1 cm, find the value of PS .

Q.

In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

Q.

Find the length of the tangent drawn from a point whose distance from the center of a circle is 25 cm. Given that the radius of the circle is 7 cm. [3 MARKS]

Q.

A quadrilateral ABCD is drawn to circumscribe a circle .If the sum of the length of sides AB + CD = 20 cm then, find the sum of the length of sides AD + BC.

1. 10 cm

2. 20 cm

3. 40 cm

4. 50 cm

Q. In the given figure PA = 4 cm and PB = 9 cm, the value of PT is equal to

1. 5 cm
2. 6 cm
3. 7 cm
4. 4 cm

Q. In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1cm, then find the value of PS.

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 and S respectively. If $AB=11cm,BC=xcm,CR=4cm$ and $AS=6cm,$ the value of $x$ is ___ $cm.$

Q. In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1cm, then find the value of PS.

Q. In the adjoining figure, $O$ is the centre of the circle and $B$ is a point of contact. Seg $OE\perp$ seg $AD$, $AB=12,AC=8$, find
i. $AD$
ii. $DC$
iii. DE.

Q. In the given figure PA = 3 cm and PT = 4 cm, the value of PB is equal to

Q. In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1 cm, then find PS. [2 Marks]