Question

in the compass and straightedge construction shown, a and b are centers of the two circles. a. name two line - segments that are perpendicular. b. name a pair of line segments with the same length. an = bm

Explanation:

Step1: Recall perpendicular lines property

Perpendicular lines intersect at a 90 - degree angle. In compass - and - straightedge construction of two intersecting circles with centers A and B, the line segment joining the centers (AB) and the common chord (the line segment connecting the intersection points of the two circles) are perpendicular.

Step2: Recall congruent line - segments property

In a symmetric construction of two intersecting circles with equal radii (if constructed that way), radii of the same circle or equal - radius circles are equal. For example, if the circles have the same radius, any radius of one circle is equal to any radius of the other circle.

Answer:

a. The line segment joining the centers A and B and the common chord of the two circles are perpendicular.
b. Let the radius of circle A be \(r_A\) and of circle B be \(r_B\). If \(r_A = r_B\), then \(AM=BN\) (where M and N are points on the circumferences of circle A and circle B respectively and are part of the symmetric construction).