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BITSAT2018MathematicsCircleActual

The area of the triangle formed by joining the origin to the point of intersection of the line x 5 + 2 y = 3 5 and circle x 2 + y 2 = 10 is

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

C. 5

Step-by-step solution

Length of perpendicular from origin to the line x 5 + 2 y = 3 5 is O L = 3 5 5 2 + 2 2 = 3 5 9 = 5 Radius of the given circle = 10 = O Q = O P P Q = 2 Q L = 2 O Q 2 - O L 2 = 2 10 - 5 = 2 5 Thus, area of Δ O P Q = 1 2 × P Q × O L = 1 2 × 2 5 × 5 = 5 sq units Hence, option (c) is correct.

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