First slide

Definition of a circle

Question

Two tangents to the circle $x^{2} + y^{2} = 4$ at the points A and B meet at P (- 4, 0). The area of the quadrilateral $P A O B$ , where O is the origin, is

Moderate

A

4
B

$6 \sqrt{2}$
C

$4 \sqrt{3}$
D

none of these

Solution

Area of quadrilateral PAOB
= 2 ( Area of triangle OAP)
$= 2 (\frac{1}{2} \times P A \times P O \sin θ) = P A \times P O \times \sin θ$
$P A = \sqrt{4^{2} + 0^{2} - 4} = 2 \sqrt{3}, P O = 4 and, \sin θ = \frac{O A}{O P} = \frac{2}{4} = \frac{1}{2}$
$∴$ Area of quadrilateral $P A O B = 2 \sqrt{3} \times 4 \times \frac{1}{2} = 4 \sqrt{3}$ sq. units.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App