Latest Elitmus Aptitude Question SOLUTION: Elitmus ( 7/01/2018) Location : Mumbai A circle is inscribed in a equilateral triangle ABC. Another smaller circle is drawn such that AB and BC are tangents to the smaller circle.

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(#M40165119) ELITMUS Numerical Ability question Geometry Keep an EYE

Elitmus ( 7/01/2018) Location : Mumbai

A circle is inscribed in a equilateral triangle ABC.
Another smaller circle is drawn such that AB and BC are tangents to the smaller circle. What is the ratio of the area of larger circle to the area of smaller circle?

Asked In Elitmus INDRAJA NAIK (6 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

  (6 years ago)

ans 9:1
was this an ans option ??

Is this solution Helpfull? Yes (4) | No (3)  

Aradhana dubey  (6 years ago)

Question is incomplete as there can be many smaller circles.

Is this solution Helpfull? Yes (3) | No (3)  

tavan  (6 years ago)

1:1 as inscribed circle also touches all the three sides of triangle and act as tangent.

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Akshay Patil  (6 years ago)

6:1 u can divide equilateral triangle into 9 equal smaller triangles based on that v can determine circles areas

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ASHFAQUE RAZA ANSARI  (6 years ago)

let side of equilateral triangle be x;
So the median of triangle is sqrt of (x^2 - (x/2)^2) = (x/2)*3^1/2;
radius of smaller circle (r) = (x/4)*3^1/2;
then radius of larger circle (R) =sqrt of ((x/2)^2 + ((x/4)*3^1/2)^2) = (x/4)*7^1/2;
ratio if larger circle and smaller circle = 7:3

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rahul  (2 years ago)

solution of this question cannot be explained clearly without the help of diagram.
so visit the link I have posted my solution there.
https://www.quora.com/A-circle-is-inscribed-in-an-equilateral-triangle-ABC-Another-smaller-circle-is-drawn-such-that-it-has-tangents-AB-and-BC-What-is-the-ratio-of-the-area-of-the-larger-circle-to-that-of-smaller-circle/answer/Rahul-Kumar-31510?prompt_topic_bio=1

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Digesh Singh Bisht  (1 year ago)

There is a theory in geometry that states that radius of smaller circle will always be 1/3 of bigger circle.
so let bigger circle has Radius (R)=3
then smaller will be radius (r) =1
Now area will be = pie* R^2/pie*r^2
ratio =9/1 ans.

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