CBSE Class 9 Answered
circles
Asked by hemant2020 | 04 Feb, 2010, 09:11: PM
Expert Answer
let ABC be the right triangle right angled at B.
let O be the mid pt of the hypo. AC.
thru' O draw line parallel to BC meeting AB on P.
so,
AP=PB.. conv of mid pt theorem
Angle OPA=OPB=90 each as line OP II BC and angle B is 90 degrees.
now consider triangles OAP and OBP,
we have
AP=PB
OP=OP.. common
angel OPA=OPB.. each 90 degrees.
so the triangles are cong.... RHS rule.
OA=OB...CPCT
but OA=OC.. since O is mid pt of AC
so we get
OA=OB=OC
Hence proved.
Answered by | 04 Feb, 2010, 11:32: PM
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