Complete the two-column proof to prove that the chords from congruent circles with corresponding congruent minor arcs are congruent. Be guided by the statements and reasons already provided for you. Given: OT ON .T AB = OE Prove: AB = OE E Proof: Statement Reason 1. 1. Given 2. mAB = mOE 2.

Let AB=a and BC=b. Point M is the midpoint of BC. If AN=23(AB), find the length of NM in terms of a and b.

Prove: In a circle containing two unequal chords, the longer chord corresponds to the larger central angle. HINT: You may use any theorems stated in this section.

a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.