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

Question

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

Philoid · Accepted Answer

ΔPOR is a right triangle because ∠O = 90°.

In a right angled triangle

(Hypotenuse)² = (Base)² + (Height)²

where hypotenuse is the longest side.

(PR)² = (OP)² + (OR)²

⇒ PR² = (6) ² + (8) ²

⇒ PR² = 36 + 64 = 100

⇒ PR = 10 m

Now, PR² + PQ² = 10² + 24² = 100 + 576 = 676

Also, QR² = 26² = 676

⇒ PR² + PQ² = QR²

which satisfies Pythagoras theorem.

Hence, ∆PQR is right angled triangle.