Question 1
In a right trapezoid $ABCD$ with right angles at the vertices $A$ and $B$ there are two circles. One of them is tangent to the legs and to the larger base $AD$, and the other is tangent to the legs, to the smaller base $BC$ and to the first circle.
1) The line through the centers of the circles meets $AD$ at the point $P$. Prove that $\frac{AP}{PD} = \sin (\angle D)$.
2) Find the area of the trapezoid if the radii of the circles are $\frac{4}{3}$ and $\frac{1}{3}$.
1) The line through the centers of the circles meets $AD$ at the point $P$. Prove that $\frac{AP}{PD} = \sin (\angle D)$.
2) Find the area of the trapezoid if the radii of the circles are $\frac{4}{3}$ and $\frac{1}{3}$.