Question : In a triangle PQR, $\angle$Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circumcircle of the triangle?
Option 1: $5$
Option 2: $6$
Option 3: $6.5$
Option 4: $6\sqrt2$
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Correct Answer: $6.5$
Solution : Given: In a triangle PQR, $\angle$Q=90°, PQ = 12 cm, and QR = 5 cm. Let the hypotenuse of the triangle be $h$ cm. So, $h^2=12^2+5^2$ ⇒ $h=\sqrt{169}$ ⇒ $h=13$ cm We know, The circumradius of a right-angled triangle is half of its hypotenuse. So, the circumradius = $\frac{13}{2}$ = 6.5 cm Hence, the correct answer is $6.5$.
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Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.
Question : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:
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