MathDB

17

Part of 2019 BMT Spring

Problems(1)

area among 2 segments and an arc 2019 BMT Individual 17

Source:

1/5/2022
Let CC be a circle of radius 11 and OO its center. Let AB‾\overline{AB} be a chord of the circle and DD a point on AB‾\overline{AB} such that OD=22OD =\frac{\sqrt2}{2} such that DD is closer to A A than it is to B B, and if the perpendicular line at DD with respect to AB‾\overline{AB} intersects the circle at EE and FF, AD=DEAD = DE. The area of the region of the circle enclosed by AD‾\overline{AD}, DE‾\overline{DE}, and the minor arc AEAE may be expressed as a+bc+dπe\frac{a + b\sqrt{c} + d\pi}{e} where a,b,c,d,ea, b, c, d, e are integers, gcd (a,b,d,e)=1(a, b, d, e) = 1, and cc is squarefree. Find a+b+c+d+ea + b + c + d + e
number theorygreatest common divisorgeometry