Two circles intersect at points 𝑋 and 𝑌 such that their common chord 𝑋𝑌 subtends 60° at the center of one circle and 90° at the center of the other. If the difference between the areas of the two circles is 12 sq cm, then find the sum of the areas of the two circles (in sq cm).

The common chord XY is of equal length in both circles, so equating the chord formulas 2 R1 sin(30) and 2 R2 sin(45) gives R1 equal to the square root of 2 times R2. Substituting this into the given area difference, pi times R1 squared minus pi times R2 squared equals 12, we get pi times R2 squared equals 12. The sum of the areas is pi times R1 squared plus pi times R2 squared, which simplifies to 3 times pi times R2 squared. Replacing pi times R2 squared with 12 gives the total sum of the areas as 36 square centimeters.

• Thanks
• Wrong explanation