QQuestion
O is a point inside a rectangle ABCD such that OB = 6 cm, OD = 8 cm and OA = 5 cm. Find OC.
✓Answer
In a rectangle, the sum of the squares of the distances from any interior point to two opposite vertices equals the sum of the squares of the distances to the other two vertices.
Thus, OA² + OC² = OB² + OD².
Substitute the given values:
5² + OC² = 6² + 8²
or, 25 + OC² = 36 + 64 = 100
or, OC² = 100 – 25 = 75
or, OC = √75 = 5√3 cm.
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