The circle as shown in the picture below, with center P and radius 2, is tangent to three sides of the rectangle ABCD. Given that the total area of the rectangle is 32, find the distance between the point P and the diagonal AC.
a) b) c) d) e)
(A)
AB is the diameter of the circle whose center is O and the triangle ABC is inscribed in. The quotient where the area of the triangle ACO is divided by the area of the triangle COB is:
a) b) c) d) e)
(D)
(FESP - 1991) An equilateral triangle ABC is inscriibed in a circle whose radius is 6 cm length. The triangle is intercepted by a diameter MN of the circle, forming a trapezoid, as shown in the picture below. We can say that the quotient of the triangle ABC area divided by the trapezoid APQC area is:
a) b) c) d) e)
(B)
The picture shows the rhombus ABCD and the point A is the center of the circle that has a 4 cm length radius. Find the area of the rhombus in square centimeters.
a) b) c) d) e)
(D)
In the following picture: is the diameter of the sphere whose center is , é is the center of a intersection with a plane perpendicular to . Also the measures are and . Calculate the area of the cicle whose center is .
The area is
Find the lateral area, the total area and the volume of a circular cone that is circumscribed to a sphere of radius and whose axial cut is an equilateral triangle.