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Triangle ABC is inscribed in the semicircle above. If the length of s
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08 Apr 2024, 22:58
08 Apr 2024, 22:58
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Triangle ABC is inscribed in the semicircle above. If the length of side AB is 10, and the length of side BC is 24, what is the area of the shaded region?
A. \(169 \pi\)
B. \(84.5 \pi\)
C. \(169 \pi - 120\)
D. \(84.5 \pi - 120\)
E. \(120\)
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Triangle ABC is inscribed in the semicircle above. If the length of s
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09 May 2024, 11:16
09 May 2024, 11:16
1
A triangle inscribed in a circle with the diameter as its hypotenuse is a right triangle. We can use the Pythagorean theorem to find the length of AC.
Let x = the length of AC / the circle's diameter
\(10^2 + 24^2 = x^2\)
\(676 = x^2\)
\(x = 26\)
Now we know the radius of the circle is 13 and we can find the area of the semicircle:
\(\frac{1}{2} * \pi * 13^2 = 84.5 \pi\)
Find the area of the triangle:
\(\frac{1}{2} * 10 * 24 = 120\)
Subtract the area of the triangle from the area of the semicircle to get the answer:
\(84.5 \pi - 120\)
Let x = the length of AC / the circle's diameter
\(10^2 + 24^2 = x^2\)
\(676 = x^2\)
\(x = 26\)
Now we know the radius of the circle is 13 and we can find the area of the semicircle:
\(\frac{1}{2} * \pi * 13^2 = 84.5 \pi\)
Find the area of the triangle:
\(\frac{1}{2} * 10 * 24 = 120\)
Subtract the area of the triangle from the area of the semicircle to get the answer:
\(84.5 \pi - 120\)
gmatclubot
Triangle ABC is inscribed in the semicircle above. If the length of s [#permalink]
09 May 2024, 11:16
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