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Question
In the given figure, O is a point inside a ΔPQR such that ∠PQR such that ∠POR = 90°, OP = 6cm and OR = 8cm. If PQ = 24cm and QR = 26cm, prove that ΔPQR is right-angled.
Solution
Applying Pythagoras theorem in right-angled triangle POR, we have:
`PR^2=PO^2+OR^2`
⟹ `PR^2=6^2+8^2=36+64=100`
⟹ `PR=sqrt100=10 cm`
IN Δ PQR,
`PQ^2+PR^2=24^2+10^2=576+100=676`
And `QR^2=26^2=676`
∴` PQ^2+PR^2=QR^2`
Therefore, by applying Pythagoras theorem, we can say that ΔPQR is right-angled at P.
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