Question

tangents PQ and PR are drawn to a circle from an external point P if PQ=9 cm and angle pqr=60 degree then the length of the chord QR is<br />a)4.5cm<br />b)6cm<br />c)9cm<br />d)18cm​

Answer 1

Answer:

Step-by-step explanation:

GIVEN:

PQ & PR are 2 tangents and QO & OR are 2 radius at contact point Q & R.

Angle PQO=90°

[A TANGENT TO A CIRCLE IS PERPENDICULAR TO THE RADIUS THROUGH THE POINT OF CONTACT]

By Pythagoras theorem

PQ²= OP² - OQ²

PQ² = 13²- 5² = 169- 25= 144

PQ= √ 144= 12

PQ=12cm

PQ= PR =12cm

[The Lengths of two tangents drawn from an external point to a circle are equal]

In ∆OPQ & ∆ OPR

OQ= OR (5cm) given

OP = OP ( Common)

PQ= PR( 12cm)

Hence ∆OPQ =~ ∆OPR ( by SSS congruence)

Area of ∆OPQ =Area ∆OPR

Area of quadrilateral QORP= 2×(area of ∆ OPR)

Area of quadrilateral QORP= 2× 1/2 × base × altitude

Area of quadrilateral QORP= OR× PR

Area of quadrilateral QORP=12× 5= 60 cm²

Area of quadrilateral QORP=60cm²