Question

Assertion (A) : Two tangents of the circle $x^2+y^2=8$ at A and B meet at P(-4,0), then the area of the quadrilateral PAOB (O is the origin) is 8 sq.units.
Reason (R ): Area of quadrilateral formed by the tangents from an external point with length of tangent with radii r is 2r.

• A. A is true, R is false
• B. A is false, R is true
• C. A is true, R is true
• D. A is false, R is false

Answer 1

The correct option is A A is true, R is false

$PA=\sqrt{4^2-8}=2\sqrt{2}$

$PA=PB=2\sqrt{2}$

So, area of Quadrilateral PAOB=area of $\Delta$ OAP + area of $\Delta$ OBP

$=\frac{1}{2}\times OA\times AP+\frac{1}{2}OB\times BP$

$=2\sqrt{2}\times 2\sqrt{2}$

$=8$

SO, the statement is true.

Reason : (R) Reason is False

Area of Quadrilateral formed by the tangent from an external point with length of tangents with radical could be anything.