A B C and D are points on a circle such that ABC is a equilateral triangle and AD is the diameter of the circle,if the radius of the circle is 2cm what is the area of quadilateral ABDC? how sides of equilateral triangle if found?

Question

Answer 1

The radius of the circle is known, so drop a perpendicular from the center on the side of the triangle. It will bisect the side.(property of circle). So we will get a 60-30-90 right angled triangle. Now applying Pythagoras theorem we can find that side of triangle = 2rt3. Now since AD is diameter, angle ACD and angle BCD both should be 90 degrees. (angles in a semicircle)
So we can find the area of triangle ACD and ABD. Sumof these two areas will give us the area of quadrilateral.
Hope your doubt is cleared. If some doubt remains, please post it again.
Thanks

Answer 2

The radius of the circle is known, so drop a perpendicular from the center on the side of the triangle. It will bisect the side.(property of circle). So we will get a 60-30-90 right angled triangle. Now applying Pythagoras theorem we can find that side of triangle = 2rt3. Now since AD is diameter, angle ACD and angle BCD both should be 90 degrees. (angles in a semicircle)
So we can find the area of triangle ACD and ABD. Sumof these two areas will give us the area of quadrilateral.
Hope your doubt is cleared. If some doubt remains, please post it again.
Thanks

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A B C and D are points on a circle such that ABC is a equilateral triangle and AD is the diameter of the circle,if the radius of the circle is 2cm what is the area of quadilateral ABDC? how sides of equilateral triangle if found?