Lista de exercícios do ensino médio para impressão

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The length of the arc $\,\stackrel \frown{AB}\,$, as in the picture, is 22 cm and O is the center of the circle. The perimeter of the circle (circumference) is:

a)

990 cm

b)

67 cm

c)

176 cm

d)

88 cm

e)

none of these answers

The radius of the circle C in the picture is 16 cm and the point P is located 7 cm far from the center O.

What is the distance between P and the circunference of the circle C?

What is the radius of the following circle which center is O,

given that:

AB = 3x - 3 and

OA = x + 3.

AB = 3x - 3 and

OA = x + 3.

Find x in the following cases:

a) s is perpendicular to $\;\overline{AB}\,$

b) $\,\overline{PA}\,$ and $\,\overline{PB}\,$ are tangent segments to the circle

The circles in the picture are externally tangent. The distance between the centers $\,\overline{OC}\,$ is 28 cm and the difference between their radii is 8 cm. Find the length of each radius.

Knowing that O is the center of the circle, find x in the following cases:

a)

b)

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)

$\,2\dfrac{\sqrt{5}}{5}\,$

b)

$\,\dfrac{\sqrt{5}}{2}\,$

c)

$\,\dfrac{\sqrt{5}}{5}\,$

d)

$\,2\sqrt{5}\,$

e)

$\,3\dfrac{\sqrt{5}}{5}\,$

AB is the diameter of the circle whose center is O and the triangle ABC is inscribed in. The quotient $\,\dfrac{s}{S}\,$ where the area $\,s\,$ of the triangle ACO is divided by the area $\,S\,$ of the triangle COB is:

a)

$\,\dfrac{5}{4}\,$

b)

$\,\dfrac{4}{3}\,$

c)

$\,\dfrac{3}{4}\,$

d)

$\,1\,$

e)

$\,\dfrac{\sqrt{3}}{2}\,$

(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)

$\,\dfrac{5}{4}\,$

b)

$\,\dfrac{9}{5}\,$

c)

$\,\dfrac{9}{8}\,$

d)

$\,\dfrac{9}{4}\,$

e)

$\,\dfrac{8}{5}\,$

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)

$\,4\sqrt{3}\,$

b)

$\,8\,$

c)

$\,12\,$

d)

$\,8\sqrt{3}\,$

e)

$\,12\sqrt{3}\,$