Question
ABCD is a rectangle with AB = 12 cm and BC = 8 cm. O is
the centre of a circle touching the three sides AB, BC, and CD of the rectangle ABCD. Find the area (in cm ² ) of △ OBC.Solution
ABCD is the rectangle where AB = CD = 12 cm and BC = AD = 8 cm. EF and BC are equal and parallel to each other. EF = BC = 8 cm Hence, EO = OF = 4 cm Thus, OEC = BCE = EOG = 90° Hence, COB = 90° Considering, the square ECGO and FBGO, OB = OC = 4√2 cm Now, triangle OBC is the right-angled triangle. Hence, the area of triangle OBC =1/2 x 8 x 4 = 16 cm²
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