in the joint figure P is a point on the side BC of triangle ABC such that MP parallel to ab and NP parallel to AC if m and C be produced meet in Q prove that PQ square is equals to qb*QC
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Answer:
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Step-by-step explanation:
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PQ² = QB * QC
Step-by-step explanation:
in Δ QBN & ΔQPM
BN ║ MP ( as AB ║ MP)
=> Δ QBN ≈ ΔQPM
=> QB/QP = BN/PM = QN/QM
in Δ QNP & ΔQMC
MC ║ NP ( as AC ║ NP)
=> Δ QNP ≈ ΔQMC
=> QP/QC = NP/MC = QN/QM
QB/QP = QN/QM
QP/QC = QN/QM
=> QB/QP = QP/QC
=> QB * QC = QP²
=> PQ² = QB * QC
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