2. PQR is a triangle right angled at P and M is a
point on QR such that PM IQR. Show that
PM=QM. MR.
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Answer:
Step-by-step explanation:
ANSWER
In △PMR,
By Pythagoras theorem,
(PR)2 =(PM) 2 +(RM) 2 .......(1)
In △PMQ,
By Pythagoras theorem,
(PQ)2 =(PM)2 +(MQ)2 .......(2)
In △PQR,
By Pythagoras theorem,
(RQ) 2 =(RP) 2 +(PQ) 2 ........(3)
∴ (RM+MQ) 2 =(RP) 2 +(PQ) 2
∴ (RM)2 +(MQ)2 +2RM.MQ=(RP)2 +(PQ) 2 ....(4)
Adding 1) and 2) we get,
(PR) 2 +(PQ)2 =2(PM)2 +(RM)2 +(MQ)2 ...(5)
From 4) and 5) we get,
2RM.MQ=2(PM)2
∴ (PM) 2 =RM.MQ
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