Q16 of 27 Page 289

The point O is situated within the rectangular figure ABCD in such a way that OB = 6 cm., OD = 8cm. and OA = 5cm. Let us determine the length of OC.

Given: In a rectangle ABCD with an interior point O,


OA = 5 cm


OB = 6 cm


OD = 8 cm



We know in a rectangle ABCD with an interior point O,


OA2 + OC2 = OB2 + OD2


⇒ 52 + OC2 = 62 + 82


⇒ 25 + OC2 = 36 + 64


⇒ OC2 = 100-25 = 75


⇒ OC = √75 = 5√3 cm


Thus OC is 5√3 cm long.


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