Question

In the figure, point B is on line segment AC and lies on circle A and circle C. If the area of circle A is four times the area of circle C, then BC/AB =

A. 2pi
B. 1/4
C. pi/4
D. 1/2

Answer 1

`\sf (1)/(2)`

Step-by-step explanation:

`\sf\\\textsf{Here AB is the radius of circle A and BC is the radius of circle C.}\\\textsf{So,}\\\textsf{Area of circle A = }\pi(AB)^2\\\textsf{Area of circle C = }\pi(BC)^2\\\textsf{Given,}\\\textsf{Area of circle A = 4}* \textsf{Area of circle C}\\or,\ \pi (AB)^2=4\pi (BC)^2\\or,\ AB^2=4BC^2\\or,\ (BC^2)/(AB^2)=(1)/(4)\\\textsf{Taking square roots on both sides,}\\(BC)/(AB)=(1)/(2)`