Multiple choice

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.

  1. A is true, R is false

  2. A is false, R is true

  3. A is true, R is true

  4. A is false, R is false
Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

The circle has centre O(0,0) and radius r = sqrt(8). The length of the tangent from P(-4,0) is sqrt((-4)^2 - 8) = sqrt(8). The area of quadrilateral PAOB is twice the area of right triangle POA, calculated as 2 * (1/2) * OA * PA = sqrt(8) * sqrt(8) = 8 sq.units; thus Assertion A is true, but Reason R is false as the formula is incorrect.

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