The above shows two circles internally tangent to each other at one point.
The smaller circle is inscribed inside the region between the 2 straight lines A B , B C and the larger circle. Also A B ⊥ B C and ∣ A B ∣ = ∣ B C ∣ .
If the radius of the larger circle is 5 2 , find the radius of the smaller circle to 3 decimal places.
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R * (rt 2 +1) /rt2 =10
R * (rt2 + 1) = 10rt2
R = 10 rt2 / ( rt2 + 1 )
Nice question. To make sure that the answer is unique, it should probably be mentioned that ∣ A B ∣ = ∣ A C ∣ and that A B ⊥ A C . Most people will make these assumptions but it may be better to be explicit.
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i think i mentioned that AB is perpendicular to BC....but they removed i think when they updated it .
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Ah, o.k.. They might have removed the condition that A B and A C are the same length as well, but that is still required for the answer to be unique.
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@Brian Charlesworth – I have updated it see now
Thanks for bringing this into our attention. We have accidentally edited the problem wrongly.
A B = B D = 5 2
D C = C E = R
A C = R 2
A D = 2 × A B = 2 × 5 2 = 1 0 2
A D = R × 2 + R
R ( 1 + 2 ) = 1 0 2
R = 1 + 2 1 0 2 ≈ 5 . 8 5 8
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