Here is a diagram of a straightedge and compass construction. c is the center of one circle, and b is the center of the other. explain why length of segment bd is the same as the length of ab

In the given diagram , here are two circles .

The center of larger circle is at C and the center of the small circle is at B.

Also, the small circle is intersecting the bigger one at two points i.e. at A and D.

Since the distance from the center of the circle to its boundary is the radius of the circle.

∴ Length of AB is same as length of BD [ ∵Radii of same circle are congruent.]

The Distance from the center ( B ) of the smaller circle to its edge is the radius of the circle therefore  length BD = length AB

 From the given diagram

The smaller circle cuts through the bigger circle creating two segments BD and AB which starts from the middle of the smaller circle to the intersecting edges of the circles.

Hence the length of segment BD = length of segment AB because they both start from point B .

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12*c

step-by-step explanation: