Ex 10.2,2
Choose the correct option and give justification.
In figure, if TP and TQ are the two tangents to a circle with centre O so that POQ = 110 , then PTQ is equal to
60 (B) 70 (C) 80 (D) 90
Given POQ = 110
Here TP is a tangent.
So, OP TP
Hence, OPT = 90
Similarly , TQ is a tangent.
So, OQ TQ
Hence, OQT = 90
Now,
In quadrilateral TPOQ
PTO + OQT + PTQ + POQ = 360
Putting values
90 + 90 + PTQ + 110 = 360
90 + 90 + 110 + PTQ = 360
290 + PTQ = 360
PTQ = 360 290
PTQ = 70
Hence, PTQ = 70
Thus, Option (B) is correct

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.