If a point O in the interior of a rectangle ABCD is joined with each of vertices A, B, C and D, then OB2+ OD2will be equal toa)2 OC2+ OA2b)OC2- OA2c)OC2+ OA2d)OC2+ 2OA2Correct answer is option 'C'. Can you explain this answer?

Question

Answer

C

Answer

Solution can be easily obtained using coordinate geometry

Let the coordinates of O be (x, y)

⇒ Coordinates of A, B, C and D be (0, 0), (0, b), (l, b) and (l, 0) respectively where l and b are length and breadth of the rectangle

⇒ OB² + OD² = (x - 0)² + (y - b)² + (x - l)² + (y - 0)² [∵ Distance between two points O(x, y) and B(a, b) = √[(x - a)² + (y - b)²]

⇒ OB² + OD² = (x - 0)² + (y - 0)² + (x - l)² + (y - b)²

Similarly, Distance between points O(x, y) and A(0, 0) + Distance between the points O(x, y) and D(l, b)

⇒ OA² + OC²
∴ OB² + OD² = OA² + OC²

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