Suuppose that circles of equal diameter are packed tightly in rows inside an equilateral triangle. (The figure illustrates the case ). If is the area of the triangle and is the total area occupied by the rows of circles, show that
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Three circles with radii , , and are externally tangent to one another, as shown in the figure. Find the area of the sector of the circle of radius that is cut off by the line segments joining the center of that circle to the centers of the other two circles.
A semicircle with diameter PQ sits on an isosceles triangle PQR to form a region shaped like a two-dimensional ice-cream cone, as shown in the figure. If is the area of the semicircle and is the area of the triangle, find
Pythagorean Theorem In these exercises we use the converse of the Pythagorean Theorem (Appendix A) to show thet the given triangle is a right triangle.
41. Refer to triangle ABC in the figure below.
(a) Show that the triangle ABC is a right triangle by using the converse of the Pythagorean Theorem
(b) Find the area of the triangle ABC
is the area of the semicircle and 
is the area of the triangle, find
