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hey this is presh talwalkar a circle with radius one is tangent to two points of the parabola y equals x squared what is the area between the circle and the parabola heres a diagram to illustrate the problem we have the parabola y equals x squared and then we have a circle of radius one thats tangent to the parabola at two points the question is whats the area thats highlighted in red in between the circle and the parabola i want to thank chad fatiolo for sending me this puzzle can you figure it out give this problem a try and when youre ready keep watching the video for the solution ill proceed to find the answer in a series of three steps well first determine the center of the circle then well find the intersection points between the circle and the parabola well then calculate the area in two different ways well first find the area using addition and subtraction of simple shapes well then also solve it using an integral so lets proceed by finding the center of the circle