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प्रश्न
Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.
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उत्तर
In ∆ PQR,
PQ = 7, PR = 3, QM = 3.5, and MR = 1.5 ...(Given)
`"PQ"/"PR" = 7/3` ...(i)
`"QM"/"MR" = 3.5/1.5 = (3.5 × 10)/(1.5 × 10) = 35/15 = 7/3` ...(ii)
From (i) and (ii)
∴ `"PQ"/"PR" = "QM"/"MR"`
∴ by converse of angle bisector theorem,
∴ Ray PM is the bisector of ∠QPR.
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संबंधित प्रश्न
Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.
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∴ `square/square = square/square` .......... (I) theorem of angle bisector.
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∴ `square/square = square/square` .......... (II) theorem of angle bisector.
But `(MP)/(MQ) = (MP)/(MR)` .......... M is the midpoint QR, hence MQ = MR.
∴ `(PX)/(XQ) = (PY)/(YR)`
∴ XY || QR .......... converse of basic proportionality theorem.
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∴ `("AB")/square = square/("EB")` [from (i) and (ii)]
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