CircleHardBloom L3
Question
Equations of four circles are $(x \pm a)^{2} + (y \pm a)^{2} = a^{2}$, then:
Options
A.The radius of the greatest circle touching all the four circles is $(\sqrt{2} + 1)a$
B.The radius of the smallest circle touching all the four circles is $(\sqrt{2} - 1)a$
C.Area of region enclosed by four given circles is $(4 - \pi)a^{2}$ sq. units
D.The centres of four circles are the vertices of a square
Solution
Sol. [Key Concept: The four circles are centred at $( \pm \ a, \pm \ a)$; a circle touching all four is concentric at the origin, with radius (centre-distance)$\pm \ a$.]
$$OA = \sqrt{2}a $$Largest radius $= \sqrt{2}a + a$
Smallest radius $= \sqrt{2}a - a$
Area enclosed by circles $= (2a)^{2} - 4\left( \frac{\pi}{4}a^{2} \right) = (4 - \pi)a^{2}$
Create a free account to view solution
View Solution FreeMore Circle Questions
The x coordinates of two points A and B are roots of equation x2 + 2x − a2 = 0 and y coordinate are roots of equat...A circle touches both the axes and its centre lies in the fourth quadrant. If its radius is 1 then its equation will be ...The equation of the normal to the circle x2 + y2 = 9 at the point is-...Two lines through (2, 3) from which the circle x2 + y2 = 25 intercepts chords of length 8 units have equations...Tangents are drawn to the circle x2 + y2 = 50 from a point ′P′ lying on the x-axis. These tangents meet the ...