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Geometry Level 4

Let A C = 6 AC= 6 and N M = 8 NM = 8 be the chord of the circle as described above. What is the area of this circle if ∠ A B C = 9 0 ∘ \angle ABC = 90^\circ ?


The answer is 78.5398.

Ahmed Moh AbuBakr by Ahmed Moh AbuBakr , 22, Egypt

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2 solutions

Paola Ramírez
Jun 24, 2015

Draw an equal triangle to △ A B C \triangle ABC as the next image shows

Then ∠ A ′ M N = 90 ° ∴ A ′ M \angle A'MN=90° \therefore A'M is circle's diameter ⇒ A ′ M = 6 2 + 8 2 = 10 \Rightarrow A'M=\sqrt{6^2+8^2}=10 so circle's area is 5 2 π = 25 π ≈ 78.5398 \boxed{5^2\pi=25\pi\approx 78.5398}

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Brilliant solution!!!

Ashish Sacheti - 5 years, 11 months ago

nice solution

Ahmed Moh AbuBakr - 5 years, 11 months ago
Ahmed Moh AbuBakr
Jun 18, 2015

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice problem!

Paola Ramírez - 5 years, 11 months ago

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thank you very much

Ahmed Moh AbuBakr - 5 years, 11 months ago

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