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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?

Thanks for your time

 Oct 3, 2022
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1. Angle HCA = 44 degrees.

 

2. Ange RAC = 28 degrees.

 

3. The area of triangle LPQ is 105.

 Oct 8, 2022

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