D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2+BD2=AB2+DE2.
Two poles of heights 6 m and 11 m stand on aplane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig.). Show that
(ii) AB=AC, i.e., ABC is an isosceles triangle.
ABC is a triangle. Locate a point in the interior of ΔABCwhich is equidistant from all the vertices of ΔABC
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.