Rhombus inside a circle

Geometry Level 2

There is a rhombus of which three vertices lies on a circle on a circle, and fourth vertex at center. If area of the rhombus is 32 3 \sqrt{3} sq. cm, then find the radius of the circle in cm.


The answer is 8.

Manish Mayank by Manish Mayank , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Prashant Goyal
Aug 7, 2014

area of that rhombus will be r*r root3/2

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Jun 29, 2015

by analysis the side of the rhombus is equal to the radius and the area of the rhombus is equal to the area of an equilateral triangle x 2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Diagonal of a rhombus are at right angles. One diagonal is R cm long. The sides are also R cm long. Two semi-diagonals form a right angled triangle with one side. The sides of this triangle are is R/2 for one semi-diagonal, and R for the side of the diagonal that is the hypotenuse.
So this is a 30-60-90 triangle, area = R 2 ∗ 3 2 \displaystyle \frac{R^2 * \sqrt{3}}{2} for 1/4 of the rhombus.

Full area = 4 ∗ R 2 ∗ 3 2 = 2 ∗ R 2 ∗ 3 = 32 ∗ 3 \displaystyle 4 * \frac{R^2 * \sqrt{3}}{2}=2 * {R^2 * \sqrt{3}} = 32 * \sqrt3

R = 8 \boxed { R=8}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How to insert a diagram in this?? For posting a problem or a note we can take a PNG file and post it on it. But how to do it here or in comment?

Niranjan Khanderia - 6 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...