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Given two intersecting circles..
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Updated on: 20 Jan 2019, 11:50
Updated on: 20 Jan 2019, 11:50
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Given two intersecting circles, one with radius 15 and another with radius 25. If the distance between the two intersecting points is 20, then find the distance between the centers of the two circles?
Show: :: OA
34.09
Originally posted by Sonalika42 on 28 Aug 2016, 04:55.
Last edited by Carcass on 20 Jan 2019, 11:50, edited 1 time in total.
Last edited by Carcass on 20 Jan 2019, 11:50, edited 1 time in total.
Edited by Carcass
Re: Given two intersecting circles..
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01 Oct 2018, 13:22
01 Oct 2018, 13:22
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Expert Reply
In this case let the circles intersect at B and F respectively, as shown in figure below:
Inkedintersecting.gif [ 17.93 KiB | Viewed 6872 times ]
Now line AC is a perpedicular bisector of BF at point D and AB=15 and BC=25. Hence to find the distance we need to calculate AD and DC.
Now triangle ABD is right triangle AD=\(\sqrt{AB^2-BD^2}=\sqrt{15^2-10^2}=11.18\)
Now triangle CBD is right triangle CD=\(\sqrt{BC^2-BD^2}=\sqrt{25^2-10^2}=22.91\).
Hence total distance AC = 11.18+22.91=34.09.
The portion marked in red are properties of a circle.
Attachment:
Inkedintersecting.gif [ 17.93 KiB | Viewed 6872 times ]
Now line AC is a perpedicular bisector of BF at point D and AB=15 and BC=25. Hence to find the distance we need to calculate AD and DC.
Now triangle ABD is right triangle AD=\(\sqrt{AB^2-BD^2}=\sqrt{15^2-10^2}=11.18\)
Now triangle CBD is right triangle CD=\(\sqrt{BC^2-BD^2}=\sqrt{25^2-10^2}=22.91\).
Hence total distance AC = 11.18+22.91=34.09.
The portion marked in red are properties of a circle.
