Question

If E is the circumcenter of ∆MNP, find each measure.

If C is the incenter of ∆AMD, m∠AMC = 3x + 6, and m∠DMC = 8x – 49, find each measure.

Answer 1

In ∆MNP, the circumcenter is equidistant from the three vertices. In ∆AMD, the incenter is the intersection point of the angle bisectors. The measures of the angles can be determined using the given expressions.

Step-by-step explanation:

Step 1: In ∆MNP, the circumcenter E is the intersection point of the perpendicular bisectors of the sides of the triangle. The circumcenter is equidistant from the three vertices. Therefore, all three segments EM, EN, and EP have the same length.

Step 2: In ∆AMD, the incenter C is the intersection point of the angle bisectors of the triangle. The angle bisectors divide the angles into two congruent angles. Therefore, the measures of ∠AMC and ∠DMC are given by 3x + 6 and 8x – 49, respectively.