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. 

Answer 1

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.