मराठी

In the Given Figure Abc is a Triangle. Cp Bisects Angle Acb and Mn is Perpendicular Bisector of Bc

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प्रश्न

In the given figure ABC is a triangle. CP bisects angle ACB and MN is perpendicular bisector of BC. MN cuts CP at Q. Prove Q is equidistant from B and C, and also that Q is equidistant from BC and AC. 

आकृती
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उत्तर

Join BQ and draw perpendicular bisector of AC cutting AC at L. 

In Δ QBN and ΔQCN 

QN = QN 

BN =NC 

∠ QNB = ∠ QNC = 90 degree.

Therefore,  ∠ QBN and ∠.QCN are congruent .

Hence Q is equidistant from B and C. 

In  Δ QNC and Δ QLC 

QC= QC 

∠ QLC = ∠ QNC = 90 degree. 

∠ QCL =∠ QCN (PC being angle bisector) 

Therefore, .Δ QNC and Δ QLC are congruent. 

Therefore, QL = QN. 

Hence Q is equidistant from BC and AC. 

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पाठ 15: Loci - Exercise 16.1

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