Question

Secants NE and SF intersect each other in the exterior of the circle

at the point M. If m(arc NS) = 125º, m(arc EF) = 37º, then m∠NMS =__.

(A) 33°

(B) 88°

(C) 22°

(D) 44°​

Answer 1

Answer:

Answer

Correct option is

B

10cm

Given :

OS=5cm, OT=10cm, TR=12cm, PR=8cm

Let QP=x

△OQS∼△ORT

SQ=6cm

Also, △PTQ∼△PSR

⇒

PS

PT

=

PR

QP

⇒

6+x

20

=

8

x

⇒x

2

+6x−160=0

x=10,−16

∴ PQ=10cm.

Hence, option B is correct.