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DBV & 1 © ek इ b ‘ i e (75) |
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Answer» your answer is 36 cm in triangle BOClet D be mid point of BCso in triangle ODC (right triangle since BC is tangent)OC = hypotenuse = 3√5 cmOD = radius = 3 cm (given)so DC^2 = (3√5)^2-3^2 = 45 - 9 = 36 (pythagoras theorem)DC = 6 cm so BC = 2DC = 12 cm now the triangle ABC is equilateral since<BOC = 360/3 = 120in triangle BOC<OCB = <OBC (since OB = OC)<OCB+<OBC= 180-<BOC= 180-120= 60hence <OCB = <OBC = 30 now<ACO = <OCB since OC is angle bisectorso <ACO = 30now <ACO + <OCB = 60 = <C similarly <B = 60therefore <A = 60 hence its an equilateral triangle with side BC = 12cmhence perimeter is 12+12+12 = 36 cm |
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