If you make a center point, let's call it O, then you know that OA=OC (both radii). If you extend the line of the stair (the one parallel to the ground) out horizontally, it will eventually intersect OA. Label this point of intersection D. Now you have formed a right triangle (triangle ODC). You know that BC=AD=8. Therefore OD=OA-AD=OA-8. You also know that AB=DC=12. Using the Pythagorean theorem, you can determine the length of OC. (OA-8)^{2}+12^{2}=OC^{2}. OA^{2}-18OA+64+144 =OC^{2}. OA^{2]-18OA+208=OC^{2}. Since OC=OA (both radii), we can plug in OA for OC. OA^{2}-18OA+208=OA^{2}. Then it is merely algebra. -18OA+208=0. 18OA=208. OA=208/18. OA=104/9.
–
Michael Thew
·
3 years, 3 months ago

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@Michael Thew
–
You have everything up to the Pythagorean theorem right. You messed up here:
\[(OA-8)^{2}+12^{2}=OC^{2}\]
\[OA^{2}-18OA+64+144 =OC^{2}\]

The \(-18OA\) should be \(-16OA\). This gives the correct answer \(OA=13\).
–
Daniel Chiu
·
3 years, 3 months ago

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TopNewestIf you make a center point, let's call it O, then you know that OA=OC (both radii). If you extend the line of the stair (the one parallel to the ground) out horizontally, it will eventually intersect OA. Label this point of intersection D. Now you have formed a right triangle (triangle ODC). You know that BC=AD=8. Therefore OD=OA-AD=OA-8. You also know that AB=DC=12. Using the Pythagorean theorem, you can determine the length of OC. (OA-8)^{2}+12^{2}=OC^{2}. OA^{2}-18OA+64+144 =OC^{2}. OA^{2]-18OA+208=OC^{2}. Since OC=OA (both radii), we can plug in OA for OC. OA^{2}-18OA+208=OA^{2}. Then it is merely algebra. -18OA+208=0. 18OA=208. OA=208/18. OA=104/9. – Michael Thew · 3 years, 3 months ago

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The \(-18OA\) should be \(-16OA\). This gives the correct answer \(OA=13\). – Daniel Chiu · 3 years, 3 months ago

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– Neha Adepu · 3 years, 3 months ago

Thank you for the correct answer!Log in to reply

– Neha Adepu · 3 years, 3 months ago

Thanks a lot! It was of great help!Log in to reply

O thanks Daniel. I was wondering why it was such a messy fraction. – Michael Thew · 3 years, 3 months ago

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