MathDB

A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is

\sqrt{50}

cm, the length of

AB

is 6 cm, and that of

BC

is 2 cm. The angle

ABC

is a right angle. Find the square of the distance (in centimeters) from

B

to the center of the circle. [asy] size(150); defaultpen(linewidth(0.65)+fontsize(11)); real r=10; pair O=(0,0),A=r*dir(45),B=(A.x,A.y-r),C; path P=circle(O,r); C=intersectionpoint(B--(B.x+r,B.y),P); draw(Arc(O, r, 45, 360-17.0312)); draw(A--B--C);dot(A); dot(B); dot(C); label("

A

",A,NE); label("

B

",B,SW); label("

C

",C,SE); [/asy]

Problem Statement