Question

In the given figure, O is a point inside a ∆PQR such that ∠POR = 90°, OP = 6 cm and OR = 8 cm. If PQ = 24 cm and QR = 26 cm, prove that ∆PQR is right-angled.

Answer 1

In ∆PQR, O is a point in it such that

OP = 6 cm, OR = 8 cm and ∠POR = 90°

PQ = 24 cm, QR = 26 cm

Now,

In ∆POR, ∠O = 90°

PR² = PO² + OR²

= (6)² + (8)²

= 36 + 64

= 100

PR = 10

Greatest side QR is 26 cm

QR² = (26)² = 676

and PQ² + PR² = (24)² + (10)²

= 576 + 100

= 676

Which implies, 676 = 676

QR² = PQ² + PR²

∆PQR is a right angled triangle and right angle at P.