Answer to Question #90894 in Geometry for Vikas

Question #90894
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
1
Expert's answer
2019-06-18T09:24:12-0400

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 180o. Since all sides are equal, then

"\u2220BAD = 180^o\/3 = 60^o."

Then find the area of rhombus by the formula:


"S=a^2sin(\u2220BAD)"

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

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