Two circles with radii a and b respectively touch each other externally. Let c be the radius of a circle that touches these two circles as well as a common tangent to the two circles. Prove that 1/√c=1/√a+1/√b. 中文题意如下,两个圆半径分别为a和b,两圆在外部相接,另一圆半径为c...
are externally tangent to each other and are internally tangent to a circle of radius at points and , as shown in the diagram. The distance can be written in the form , where and are relatively prime positive integers. What is ?
radius of the larger circle is and a radius of the smaller circle is . The area of the shaded region is( ).A: B: C: D: 相关知识点: 试题来源: 解析 C The area of the shaded region is the difference in the areas of the two circles. Since Area , the shaded area . 图中...
. Thus, the diameter of the bigger circle is times that of the smaller circle. The circumference of the bigger circle is times that of the smaller circle, and the area of the bigger circle is times that of the smaller circle. We can infer that if the radius of circle ...
From each point a chord of length r is drawn in a clockwise direction. What is the probability that the two chords intersect?( )A.16B.15C.14D.13E.12 2【题目】T wo points on the circumference of a circle of radius r are selected independently and at random. Fromeach point a chord ...
A. The area of a circle is in proportion to its radius. B. The speed of light is in proportion to the time it travels. C. The number of students is in proportion to the size of the classroom. D. The weight of an object is in proportion to its color. 相关知识点: 试题...
Two points on the circumference of a circle of radius r are selected independently and at random. From each point a chord of length r is drawn in a clockwise direction. What is the probability that the two chords intersect?( ) A. 16 B. 15 C. 14 D. 13 E. 12 相关知识点: 试题...
Let the radius of the large circle be . Then the radii of the smaller circles are . The areas of the circles are directly proportional to the square of the radii, so the ratio of the area of the small circle to the large one is . This means the combined area of the smaller circles...
as the vertex and radius as the side length. Given that the area of the shaded region is , find the area of the annulus. ()相关知识点: 试题来源: 解析 The area of the annulus is . The area of the annulus is equal to the area of the big circle minus the area of the small circ...
Two circles of radius 1 are to be constructed as follows. The center of circle A is chosen uniformly and at random from the line segment joining (0,0) and (2,0). The center of circle B is chosen uniformly and at random, and independently of the first choice, from the line segment ...