Find Length of Arc EF in Triangle ABC

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In summary, we have a triangle with angle and point as the midpoint of segment with length 12 units. A circle with center and radius intersects with segments and at points and respectively. The length of arc is approximately 4.1888 units.
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Albert1
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,with point is the midpoint of segment
circle (wth center and radius , meets with at points and respectively please find the length of arc
 
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  • #2
Albert said:
,with point is the midpoint of segment
circle (wth center and radius , meets with at points and respectively please find the length of arc
[sp]
In the diagram, the angle is a right angle (angle in a semicircle). So is a right-angled triangle and . Therefore (angle at centre = twice angle at circumference). If is 12 units then the radius of the circle is 6 units, and the arc is units.

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perfect ! very good solution !
 

FAQ: Find Length of Arc EF in Triangle ABC

How do I find the length of Arc EF in Triangle ABC?

To find the length of Arc EF in Triangle ABC, you can use the formula:

Arc length = (Central angle/360) x (2πr), where r is the radius of the circle. In this case, r can be calculated using the Law of Cosines or by dividing the length of the chord by 2 and finding the square root of (r^2 - (c/2)^2).

Can I use the Pythagorean Theorem to find the length of Arc EF in Triangle ABC?

No, the Pythagorean Theorem cannot be used to find the length of Arc EF. It can only be used to find the length of the side lengths of a right triangle, not the length of an arc.

What information do I need to find the length of Arc EF in Triangle ABC?

To find the length of Arc EF, you will need the measure of the central angle and the radius of the circle. You can also use the Law of Cosines to find the radius if the side lengths of the triangle are known.

Can I use the Law of Sines to find the length of Arc EF in Triangle ABC?

No, the Law of Sines cannot be used to find the length of Arc EF. It can only be used to find the side lengths or angles of a triangle, not the length of an arc.

Are there any other methods to find the length of Arc EF in Triangle ABC?

Yes, you can also use the sector area formula: Arc length = (Central angle/360) x (πr^2), where r is the radius of the circle. Alternatively, if the triangle is inscribed in a circle, you can use the Inscribed Angle Theorem to find the length of Arc EF.

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