13am getting its radius = 2+ 4√2
Q. Of the two concentric circles the smaller one has the equation x2+y2=4. If each of the two intercepts on the line x+y=2 made between the two circles is 1, find the equation of the larger circle.
just want the answer
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8 Answers
13Thnx b555....another method....
Line intersects Bigger Circle @ X(p,q) & smaller one @ A(0,2) & B(2,0).....
Take Line XAB ; use section formula
0 = 1*2 + 2√2p => p=-1/√2
2= 2√2q/(1+2√2) => q= 2+1/√2
Radius = √(p2+q2) = √(5+2√2)
Kumar Rajadityam Give me the diagramUpvote·0· Reply ·2015-10-25 09:59:40- Kumar Rajadityam I found the result by using trigonometry but answer is coming only 2+1/√2
106hmm the answers given radius = √5+2√2 and i got the radius to be 2+1/√2
13U did using figure kya ??? Similarity of triangles ?.....i found my fault ;trying another way....
39solution:
u get the points on smaller corcle and on line as (2,0) and(0,2)
now let the points on line as well as bigger circle be (x1,y1) and (x2,y2)
now use the fact that
(2-x1)2+(-y1)2=1
x1+y1=2 to get x1 and y1
now use x12+y12=k2 where k is radius u get k as √(5+2√2)
here i have assumed the point towards (2,0) side is(x1,y1)
hope u get it
39nice method; ultimately u find coordinates of a point on bigger circle