a) Use Pythagorean theorem: One leg of the isosceles triangle is the hypotenuse, the median and the half base are the legs in a right triangle:
b) A median in a triangle is divided by the remaining medians into 2 parts with the ratio 2:1 from the vertex.
#1: If the rectangle is inscribed into a circle the diameter of the circle is a diagonal of the rectangle. Use Pythagorean theorem to calculate the length of the other side of the rectangle:
. Now calculate the area of the rectangle.
#2: Which radius?
#3: The area of a circle is calculated by:
. You have:
. and therefore
The perimeter is calculated by:
Calculate the perimeter and and build the ratio:
or more generally: