Q. 254.8( 6 Votes )

# In Fig. 7, tangen

Answer :

PR = PQ (Tangents drawn from an external point are equal)

PQR = PRQ (Angles opposite to equal sides)

In ΔPQR,

PQR + PRQ + RPQ = 180° (Sum of all angles of a triangle is 180°)

PRQ + PRQ + 30° = 180°

2PRQ = 150° Given that, RS||PQ

So, SRQ = PQR = 75° (Alternate interior angle)

Join OR and OQ.

ORP = 90° (tangent is perpendicular to the radius)

ORQ + QRP = 90°

ORQ + 75° = 90°

ORQ = 15°

In ΔORQ,

OQR = ORQ = 15° (Angles opposite to equal sides as OR = OQ = radius)

OQR + ORQ + ROQ = 180° (Sum of all angles of a triangle is 180°)

15° + 15° + ROQ = 180°

ROQ = 150°

Now, RSQ = ROQ/2 (Angle in the major sector) In Δ RSQ,

RSQ + SRQ + RQS = 180° (Sum of all angles of a triangle is 180°)

75° + 75° + RQS = 180°

RQS = 30°

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 