Question : In $\triangle$PQR, $\angle$ PQR = $90^{\circ}$, PQ = 5 cm and QR = 12 cm. What is the radius (in cm) of the circumcircle of $\triangle$PQR?
Option 1: 6.5
Option 2: 7.5
Option 3: 13
Option 4: 15
Correct Answer: 6.5
Solution : In $\triangle$ PQR, $\angle$ PQR = $90^{\circ}$, PQ = 5 cm and QR = 12 cm PR2 = PQ2 + QR2 $PR = \sqrt{5^2 + 12^2} = \sqrt{25+144} = \sqrt{169} = 13$ cm Circumradius of $\triangle PQR = \frac{PR}{2} = \frac{13}{2} = 6.5$ cm Hence, the correct answer is 6.5.
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Question : $\triangle$ PQR circumscribes a circle with centre O and radius r cm such that $\angle$ PQR = $90^{\circ}$. If PQ = 3 cm, QR = 4 cm, then the value of r is:
Option 1: 2
Option 2: 1.5
Option 3: 2.5
Option 4: 1
Question : In $\triangle$ ABC, $\angle$ BCA = $90^{\circ}$, AC = 24 cm and BC = 10 cm. What is the radius (in cm) of the circumcircle of $\triangle$ ABC?
Option 1: 12.5
Option 2: 13
Option 3: 25
Option 4: 26
Question : If AB = 5 cm, AC = 12 cm, and AB$\perp$ AC, then the radius of the circumcircle of $\triangle ABC$ is:
Option 1: 6.5 cm
Option 2: 6 cm
Option 3: 5 cm
Option 4: 7 cm
Question : The sides of $\triangle$ABC are 10 cm, 10.5 cm and 14.5 cm. What is the radius of its circumcircle?
Option 1: 5 cm
Option 2: 7.5 cm
Option 3: 5.25 cm
Option 4: 7.25 cm
Question : If $\triangle$PQR is right-angled at Q, PQ = 12 cm and $\angle$PRQ = 30°, then what is the value of QR?
Option 1: $12\sqrt{3}$
Option 2: $12\sqrt2$
Option 3: $12$
Option 4: $24$
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