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Question

Question 12
If S is a point on the side PQ of a Δ PQR such that PS = QS = RS, then

(A) (PR)(QR)=RS2
(B) QS2+RS2=QR2
(C) PR2+QR2=PQ2
(D) PS2+RS2=PR2

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Solution



Given : In ΔPQR
PS = QS = RS …(i)
In ΔPSR
PS = RS [from Eq.(i)]
1=2 ...(ii)

Similarly, in ΔRSQ
QS = RS (Given)
3=4
In ΔPQR,
P+Q+R=180 (from angle sum property of triangle)
2+4+1+3=180
1+3+1+3=180
2(1+3)=180
1+3=1802=90
R=90
ΔPQR is a right angled triangle.

Therefore, by applying Pythagoras theorem in ΔPQR, we get,
PR2+QR2=PQ2






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