Question

Triangle PQR, circumscribes a circle of radius r, such hat angle Q= 90 degrees PQ= 3 cm and QR= 4cm. Find r.

Answer 1

Solution:-

Let PQR be the right angled triangle such that ∠ Q = 90°, PQ = 3 cm and QR = 4 cm. Let O be the center and r be the radius of the circle respectively.

(Please see the figure attached)

PQ, QR and RP are tangents to the circle at C, A and B.
∴ OC = OB = OA = r (radius of the circle)
Area of the triangle PQR = 1/2 × 3 × 4
= 6 cm²
By Pythagoras Theorem,
⇒ RP² = PQ² + QR²
⇒ RP² = 3² + 4²
⇒ RP² = 9 + 16
⇒ RP² = 25
⇒ RP = √25
⇒ RP = 5 cm
Area of Δ PQR = Area of Δ OPQ + Area of Δ OQR + Area of Δ ORP
⇒ 6 = 1/2r × (PQ) + 1/2r × (QR) + 1/2r × (RP)
⇒ 6 = 1/2r(PQ + QR + RP)
⇒ r = (6*2)/(PQ + QR +RP)
⇒ r = 12/(3 + 4 + 5)
⇒ r = 12/12
⇒ r = 1 cm
Answer.

Answer 2

don't forget to mark as brainliest. .