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If the triangle ABC is inscribed in semi-circle
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15 Jun 2021, 07:59
15 Jun 2021, 07:59
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If the triangle ABC is inscribed in semi-circle BAC as above figure and BC is a diameter, the length of AB is 6 and the length of AC is 8, what is the length of arc BAC?
A. 5π
B. 6π
C. 7π
D. 8π
E. 10 π
If the triangle ABC is inscribed in semi-circle
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15 Jun 2021, 08:25
15 Jun 2021, 08:25
1
Solution:
Any triangle inscribed in a circle, which has one of the sides as its diameter is always a right triangle.
Similarly, in the above figure, using Pythagoras theorem, we can find BC=10
Circumference of the circle=πd=10π
Circumference of the semi circle=\(\frac{10π}{2}\)=5π
Arc BAC covers half of the circle and is thus a semi circle.
IMO A
Hope this helps!
Any triangle inscribed in a circle, which has one of the sides as its diameter is always a right triangle.
Similarly, in the above figure, using Pythagoras theorem, we can find BC=10
Circumference of the circle=πd=10π
Circumference of the semi circle=\(\frac{10π}{2}\)=5π
Arc BAC covers half of the circle and is thus a semi circle.
IMO A
Hope this helps!
If the triangle ABC is inscribed in semi-circle
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15 Jun 2021, 08:27
15 Jun 2021, 08:27
2
When one side is a diameter then the triangle formed will be a right triangle.
According to the Pythagoras theorem,
\(AB^2 + AC^2 = BC^2\)
\(BC = 10\) = diameter
radius = \(5\)
Length of Arc \(BAC = π * r = 5π\)
Answer A
According to the Pythagoras theorem,
\(AB^2 + AC^2 = BC^2\)
\(BC = 10\) = diameter
radius = \(5\)
Length of Arc \(BAC = π * r = 5π\)
Answer A
