In the given figure, PQ and RS are two chords of a circle intersecting each other at a point T outside the circle. If PT = 3 cm, PQ = 5 cm, RS = 2 cm, then the length of RT is

2 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
4 cm
Given : PT=3cm, PQ=5cm, RS=2 cm

$Using Secant Theorem, \Rightarrow T P \times T Q = T R \times T S \Rightarrow 3 \times (3 + 5) = T R \times (T R + 2) \Rightarrow T R^{2} + 2 T R - 24 = 0 \Rightarrow T R (T R + 6) - 4 (T R + 6) = 0 \Rightarrow (T R - 4) (T R + 6) = 0 \Rightarrow T R = 4 o r T R = - 6$
(Rejecting negative value)
Thus, the length of TR is 4 cm.

Hence, the correct answer is option c.

Suggest Corrections

Similar questions

Q. PQ and RS are chords of a circle which intersect at O outside the circle. If PQ = 5 cm, OQ = 9 cm and RS = 15 cm, then the length of OS is

Q. Two chords PQ and RS intersect at point O inside the circle. If OP = 4 cm, OQ = 9 cm and RS = 12 cm, then the value of OR is .

In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is

Q. Chords MN and RS of a circle intersect at P outside the circle. If

P N = 3 c m, M N = 5 c m, P R = 2 c m

, then the value of SR is equal to

Join BYJU'S Learning Program

In the given figure, PQ and RS are two chords of a circle intersecting each other at a point T outside the circle. If PT = 3 cm, PQ = 5 cm, RS = 2 cm, then the length of RT is

The correct option is C 4 cmGiven : PT=3cm, PQ=5cm, RS=2 cm Using Secant Theorem,⇒TP×TQ=TR×TS⇒3×(3+5)=TR×(TR+2)⇒TR2+2TR−24=0⇒TR(TR+6)−4(TR+6)=0⇒(TR−4)(TR+6)=0⇒TR=4 or TR=−6 (Rejecting negative value) Thus, the length of TR is 4 cm. Hence, the correct answer is option c.