Answer to Question #90894 in Geometry for Vikas

Question

A rhombus ABCD has side of length 10 .a circle with center A passes through C and similar for center B And passes through D.
If two circles are tangent to each other find area of rhombus

Answer 1

Two circles are tangent to each other inner way. Since the condition B is the center of the second circle, then AB, BD and BC are radii of the second circle, besides, ABCD is a rhombus. Therefore, ABD is an equilateral triangle. The sum of angles in a triangle is 180^o. Since all sides are equal, then

$∠BAD = 180^o/3 = 60^o.$

Then find the area of rhombus by the formula:

$$S=a^2sin(∠BAD)$$

$S = 10^2*sin(60^o)$ = $50\sqrt3$