Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Sunday, February 8, 2015

### Geometry Problem 1080: Square, Circle, Tangent, Side, Radius, Metric Relations

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√2 a = AC

ReplyDelete= AH + HO + OC

= √2 GH + HO + √2 HO

= 2√2 HO + HO + √2 HO

= (3√2 + 1)HO

HO = √2 a / (3√2 + 1) = (6 - √2)a/17

EF = 2(1+√2)(6 - √2) a/17 = 2a (4+5√2)/17

http://s21.postimg.org/us94eayo7/pro_1080.png

ReplyDeleteLet MD=y and OH=r

We have y= r+r/√2

Or r=2.y/(2+√2)

We have 2.r= GH= a-y

So 4.y/(2+√2)= a-y => y= a/(1+4/(2+√2))

EF=2.y√2= (4+4√2).a/(6+√2)

So EF=2.a*(4+5. √2)/17