## Sample 2nd Midterm

1. Prove one of
the theorems about isosceles triangles

2. Prove
another of the theorems about isosceles triangles.

3. Given that __/__AOE =
38^{o}, O is the center of the circle, NO__ | __OE, NO ||
AP, and NE is tangent to the circle at A,

.find __/__NAP

4. Given a
triangle, construct the three perpendicular bisectors, the three
angle bisectors, the three medians and the three altitudes. Draw in
the circumscribed circle, the inscribed circle, and the Euler line.

5. Given that DE
|| BC, AB = 8, BC = 12, AD = 5, find DE.