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Shank18
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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It came using similar triangle property as attached here.
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Geometry 7 Similar Triangle Latest.jpg
Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 3163 times ]

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GMATinsight
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Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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It came using similar triangle property as attached here.



Thank you so much. This is exactly what I needed
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https://gmatclub.com/forum/if-arc-pqr-a ... 44057.html

Bunnel and other experts posted great detailed solution for similar problem in the above link.

Hope it helps :)
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ShankSouljaBoi
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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You can also approach it algebraically.

\(c^2=\)hypotenuse big triangle
\(d^2=\)hypotenuse small triangle


\( a^2+1= c^2\)
\(b^2+1= d^2\)
Substitution \( c^2+d^2= 〖(a+b)〗^2\)
Expansion of the quadratic \(a^2+1+b^2+1=a^2+2ab+b^2\)
Simplification \(2=2ab -----> 1=ab\)


I hope this helps
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