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#1 2015-01-14 10:10:24
- SPARKS_CHAN
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- Registered: 2014-12-05
- Posts: 15
Geo problems!
1) In the figure with four circles below, let A_1 be the area of the smallest circle, let A_2 be the area of the region inside the second-smallest circle but outside the smallest circle, and so on. If A_1 : A_2 : A_3 : A_4 = 1 : 2 : 3 : 4, then find the ratio of the largest radius to the smallest radius.
2) In triangle ABC, AB = 5, AC = 6, and BC = 7. Circles are drawn with centers A, B, and C, so that any two circles are externally tangent. Find the sum of the areas of the circles.
3) Let ABCD be a square of side length 4. Let M be on side BC such that CM = 1, and let N be on side AD such that DN = 1. We draw the quarter-circle centered at A.
Let x and y denote the areas of the shaded regions, as shown. Find x - y.
Last edited by SPARKS_CHAN (2015-01-15 06:59:15)
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#2 2015-01-14 13:06:21
- ElainaVW
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- Registered: 2013-04-29
- Posts: 580
Re: Geo problems!
Hello,
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#3 2015-01-14 13:49:06
- SPARKS_CHAN
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- Registered: 2014-12-05
- Posts: 15
Re: Geo problems!
Can someone explain to me why the answer to number one isn't 2:1?
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#4 2015-01-15 07:00:05
- SPARKS_CHAN
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- Registered: 2014-12-05
- Posts: 15
Re: Geo problems!
Got the answer for 1!
It's sqrt10:1.
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#5 2015-01-15 07:26:21
- Olinguito
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- Registered: 2014-08-12
- Posts: 649
Re: Geo problems!
3) Let ABCD be a square of side length 4. Let M be on side BC such that CM = 1, and let N be on side AD such that DN = 1. We draw the quarter-circle centered at A.
Let x and y denote the areas of the shaded regions, as shown. Find x - y.
Let z be the area of the quarter-circle bounded by DN, MN and the arc. Then
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It should be straightforward to find x−y.
Bassaricyon neblina
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