Question 601836
Hello dear,
In order to solve this problem, you have to first find the angle made by the arc BCD at the center of the circle,
Then use the formula to find the length of the arc
i.e. Length of arc = (π*r*θ)/180

where 'θ' is the angle made by the arc at the center,
'r' is the radius of the circle.


Using this formula, find the radius and then the area of the circle.
Area of circle = (π*r^2)


THE SOLUTION

AE is parallel to BD,
So angle EAD = angle ADB (because these are interior alternate angles)
So angle ADB = 30 degrees


Let 'O' be the center of the circle, so it must lie on the diameter AD.
Join OB

Now in triangle OBD,
OB = OD [radii of the circle]
As you know, the angles opposite to the equal sides of a triangle are equal,
So, angle ODB = angle OBD
But angle ODB (OR ADB) = 30 degrees
So angle OBD = 30 degrees

Now using the angle sum property of a triangle, we will find the measure of angle BOD which is 120 degrees

Now Length of arc = (π*r*θ)/180


Solving this, we get r = 6 units

Area of circle = (π*r^2)
= 3.14*6*6
= 113.14 square units



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