Circles A. B, and C cach have raditus 1. Circles A and B share one point of tangency. Circle C has a point of tangency with the midpoint of AB―. What is the area inside circle C but outside circle A and circle B?a) 3−π2b) π2c) 2d) 3π4e) 1+π2

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Pooja Copeland · Accepted Answer

Stpe 1Given, Circles A, B, and C each have radius 1. Circles A and B share one point of tangency.Circle C has a point of tangency with the midpoint of AB―.To find the are inside circle C but outside A and circle B, that is, the shaded region of the circle C.Now, Area of shaded region=Area of Circle C−Area shared between Circles A, B and C.Let S be the mid point of AB― and T be the point of intersection of Circles A and C.Join the points by joining the points STStep 2Now, the shared area of all three circles A, B, C=4 X the region between line ST and arc ST.The area of the Circle A=πr2=πThe area of△SAT=12bh=12 since b=h=r=1So, the area between the line ST and the arc ST=14× (Area of Circle A) - Area of △SAT=14×π−12=(π−24)Step 3Area of Shaded region in Circle C=(Area of Circle C )−4 (Area between the line ST and the arc ST)=π(1)2−4(π−24)=π−π+2=2Therefore, Area of Shaded region in Circle C is 2.

Circles A. B, and C cach have raditus 1. Circles

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