The radius of the incircle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6cm and 8 cm .Determine the other two sides of the triangle.

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The radius of the incircle of a triangle is 4 centimetre and the segment into which one side is divided by the point appointed assistant University M determine the two sides of the triangle

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Let the given circle touch the sides AB and AC of the triangle at point E and F respectively and the length of the line segment AF bex. In ABC, CF = CD = 6cm (Tangents on the circle from point C) BE = BD = 8cm (Tangents on the circle from point B) AE = AF = x (Tangents on the circle from point A) AB = AE + EB = x + 8 BC = BD + DC = 8 + 6 = 14 CA = CF + FA = 6 + x 2s = AB + BC + CA = x + 8 + 14 + 6 + x = 28 + 2x s = 14 + x Area of ΔOBC = Area of ΔOCA = Area of ΔOAB = Area of ΔABC = Area of ΔOBC + Area of ΔOCA + Area of ΔOAB Either x+14 = 0 or x − 7 =0 Therefore, x = −14and 7 However, x = −14 is not possible as the length of the sides will be negative. Therefore, x = 7 Hence, AB = x + 8 = 7 + 8 = 15 cm CA = 6 + x = 6 + 7 = 13 cm THUMBS UP PLEASE

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