Geometry: Internal Bisector of an Angle of a Triangle
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 Internal Bisector of an Angle of a Triangle The internal bisector of an angle of a triangle divides the side opposite to it, internally in the ratio of the sides containing the angle.
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Example: In fig. below, PM is the bisector of QPR. If PQ = 12 cm, PR = 16 cm and QR = 8 cm, find QM and MR.
 Solution: Let QM = x cm. Then, MR = (8 - x)cm. As PM is the bisector of P. So     PQ/PR = QM/MR 12/16 = x/(8 - x) 3/4 = x/(8 - x) 24 - 3x = 4x 7x = 24 x = 24/7 x = 3.43 cm Therefore, QM = 3.43 cm MR = (8 - x) = (8 - 3.43) = 4.57 cm.

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