+30 In triangle ABC, point M is the midpoint of segment AB Let D be the point on segment BC such that segment AD bisects angle BAC, and let the perpendicular bisector of segment AB intersect segment AD at point E. If AB = 44, AC = 30, and ME = 10 then find the area of triangle ACE.
+1632 Time to tackle this tough reposted question!
By pythagorean theorem, CE = sqrt(30^2 - 22^2) - 10. CE = 4sqrt(26) - 10. Then by pythagorean theorem, AE = sqrt(22^2 + 10^2) = 2sqrt(146). Now we know the side lengths of triangle ACE are 30, 4sqrt(26) - 10, and 2sqrt(146) respectively. Using heron's formula, the area of triangle ACE would approximately be 114.357.
