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
Correct Answer: 6.5 cm
Solution : Given: $AB = 5$ cm; $AC = 12$ cm and $AB \perp AC$ $BC$ = Diameter In $\triangle ABC$, $BC = \sqrt{AB^2 + AC^2}$ $BC = \sqrt{5^2 + 12^2} = \sqrt{25 + 144}$ $BC = \sqrt{169} = 13 \;cm$ $\therefore OB$ is the radius = $\frac{BC}{2}=\frac{13}{2}=6.5$ cm Hence, the correct answer is $6.5$ cm.
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Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:
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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?
Question : Let $\triangle {ABC} \sim \triangle {RPQ}$ and $\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle P Q R)}=\frac{4}{9}$. If ${AB}=3 {~cm}, {BC}=4 {~cm}$ and ${AC}=5 {~cm}$, then ${PQ}$ (in ${cm}$ ) is equal to:
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