Please provide solutions if possible.
Happy Problem solving !!
Prove that in a right triangle, the bisector of right angle halves the angle between the median and the altitude drawn from the same vertex.
Prove that if in a triangle, the ratio of tangents of two angles is equal to the ratio of squares of the sines of these angles, then the triangle is either an isosceles or a right one.
Straight lines are parallel, lying between and at a distance of and from them. Find the size of a regular triangle whose vertices lie on the given lines (one on each line).
The diagonal of a rectangle divides its angle in the ratio . Find the ratio of the perimeter of the rectangle to its diagonal.
The acute angle of a parallelogram is equal to and the sides are and . Find the tangent of the acute angles formed by the larger diagonal and the sides of the parallelogram.