Question : If PT is a tangent at T to a circle whose centre is O and OP = 17 cm and OT = 8 cm, find the length of the tangent segment PT.

Option 1: 13 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 15 cm

Question : Point O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, point P is taken. From this point, two tangents, PQ and PR, are drawn to the circle. Then, the area of quadrilateral PQOR is:

Option 1: $60\ \text{cm}^2$

Option 2: $32.5\ \text{cm}^2$

Option 3: $65\ \text{cm}^2$

Option 4: $30\ \text{cm}^2$

Question : The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is:

Option 1: 5 cm

Option 2: 6 cm

Option 3: 7 cm

Option 4: 8 cm

Question : The chords PQ and RS of a circle, when produced, meet at a point O. If PQ = 6 cm, OQ = 8 cm, and OS = 7 cm, then the length (in cm) of the chord RS is:

Option 1: 10

Option 2: 12

Option 3: 16

Option 4: 9

Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

Option 1: $5 \sqrt{5}$ cm

Option 2: $5 \sqrt{2}$ cm

Option 3: $5$ cm

Option 4: $5 \sqrt{3}$ cm