1) Altitudes AD and BE of acute triangle ABC intersect at point H. If angle AHB = 128 degrees and angle BAH is 28 degrees, then what is angle HCA in degrees?
2) Triangle ABC is a right triangle with angle BAC = 90 degrees and angle B is greater than angle C. Suppose segment AP is an altitude of the triangle, segment AQ is an angle bisector of the triangle, and segment AR is a median of the triangle, and angle PAQ is 13 degrees. If P is on segment BQ, then what is the measure of angle RAC?
3) Points M, N, and O are the midpoints of sides KL, LJ, and JK respectively of triangle JKL. Points P, Q, and R are the midpoints of segments NO, OM, and MN respectively. If they are of triangle PQR is 27, then what is the area of triangle LPQ?
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