Elitmus 7 01 2018 Location Mumbai A circle is inscribed in a equilateral triangle ABC Another smaller circle is drawn

Question is incomplete as there can be many smaller circles.
6 years agoHelpfull: Yes(3) No(3)
1:1 as inscribed circle also touches all the three sides of triangle and act as tangent.
6 years agoHelpfull: Yes(0) No(3)
6:1 u can divide equilateral triangle into 9 equal smaller triangles based on that v can determine circles areas
6 years agoHelpfull: Yes(0) No(1)
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
6 years agoHelpfull: Yes(0) No(0)
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
2 years agoHelpfull: Yes(0) No(0)
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.
1 year agoHelpfull: Yes(0) No(0)

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?