Multiple Choice Questions on For a triangle the radius of the circumcircle is double the radius of the inscribed circle then whic........... for CDS Exam Preparation

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Multiple Choice Questions

For a triangle the radius of the circumcircle is double the radius of the inscribed circle then whic...........

Quantitative Aptitude (CDS) Coordinate Geometry
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    For a triangle, the radius of the circumcircle is double the radius of the inscribed circle, then which one of the following is correct?

    The triangle is a right-angled

    Incorrect Answer

    The triangle is an isosceles

    Incorrect Answer

    The triangle is an equilateral

    Correct Answer

    None of the above

    Incorrect Answer
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    Explanation:

    Here, OD is the radius of in circle while OB is the radius of outer circle. Given that Radius of outer circle = 2 x radius of incircle.

    ⇒ OB = 2 × OD
    ⇒ (OB/OD) = 2 ⇒(OD/OB) = (1/2)
    ⇒ Sin\angle BDO\:= \frac{1}{2}=sin 30^{o} =

    \angle DBO = 30^{o}, \angle ABC = 2 × \angle DBO = 2 × 30^{o} = 60^{o}

    So, it is equilateral triangle.

    By: Munesh Kumari
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