In ∆PQR right angled at Q, PQ = QR. If QS ⊥ PR, then the length of PS is not equal to
Answers
Given : In ∆PQR right angled at Q, PQ = QR.
QS ⊥ PR,
To Find : the length of PS is not equal
PQ
QS
RS
Solution:
In ∆PQR right angled at Q, PQ = QR.
=> ∆PQR is isosceles right angles triangle
QS ⊥ PR
=> QS will be the median also
As circumcenter of right angle triangle lies on mid point of hypotenuse
Hence PS = RS = QS = Radius of the circle
and PS = PR/2
PR = √PQ² + QR²
PS = √PQ² + QR²/2
=> 2PS = √PQ² + QR²
=> 4PS² = PQ² + QR²
QR = PQ
=> 4PS² = 2PQ²
=> PS² = PQ²/2
=> PS = PQ/√2
Hence PS is not equal to PQ
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