If ∠ A = 6 0 ∘ , then △ A BC is

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Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of Triangler1,r–R formula basedMedium2 minQB

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Passage / Comprehension

Let ABC be a triangle in which the line joining the circumcentre and incentre is parallel to base BC of the triangle, making use of the standard notation $r$ and $R$ .

If $∠ A = 6 0^{\circ}$ , then $△ A BC$ is

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Answer:

Solution:

$\frac{r}{R} = cos A = \frac{1}{2}$ . But $\frac{r}{R} \leq \frac{1}{2}$ in any triangle, with equality only for an equilateral triangle. Hence $△ A BC$ is equilateral.

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:r1,r–R formula based

⏱ 2mℹ️ Source: QB

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