A lateral side of an isosceles triangle is $15 cm$ and the altitude is $8 cm$. What is the radius of the circumscribed circle

In the given figure

$AB=20$

$BC=15$

$CA=19$

Calculate $a,b,c$

In the figure given below, $AB$ is perpendicular to $ED$. $\angle CED={75}^o$ and $\angle ECF={30}^o$. What is the measure of $\angle ABC$?

The angle between lines $L$ and $M$ measures ${35}^o$ degrees. If line $M$ is rotated ${45}^o$ degrees counter clockwise about point $P$ to line $M^1$ what is the angle in degrees between lines $L$ and $M^1$

In the figure given below, $XYZ$ is a right angled triangle in which $\angle Y={45}^o$ and $\angle X={90}^o$. $ABCD$ is a square inscribed in it whose area is $64 c{m}^2$. What is the area of triangle $XYZ$?

Find the area of the shaded portion