C'mon! Archery is Irrelevant here!

Geometry Level 3

There are 3 concentric circles with center O O and radii 3 , 5 , 7 3,5,7 units.

Points A , B , C A,B,C are on these circles, one on each circle.

Find the minimum value of A B + B C + C A AB+BC+CA

Also see

Remember the Aim in Archery?

There's no Archery without Aim!

Only looks like Archery Aim!


The answer is 8.

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Aditya Raut by Aditya Raut , 23, India

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2 solutions

Deepanshu Gupta
Mar 10, 2015

Let's Fixed A ( 3 , 0 ) A(3,0) then clearly minimum occur when All three Points are collinear. And Hence for this purpose B ( 5 , 0 ) B(5,0) and C ( 7 , 0 ) C(7,0) .

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Can you tell me when does the maximum occur?

Rama Devi - 6 years ago

All three points on the same radial line of the biggest circle on the same side of the center.
Say ABC from short radius circle to middle and big. AB+BC+AC=5-3 + 7-5 + 7-3= 2 + 2 + 4 = 8.

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