Triangle in a Circle w/ area 1891.59sq mtrs

rubbishatmaths

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1. I have an equilateral triangle in a circle and each of the points of the triangle are touching the circle. The inner circle area is 1891.59sq mtrs. How long is each side of the triangle?
2. I have an equilateral triangle inside a circle with each triangle side measuring
51.89mtrs, each point of the triangle touches the circle. What is the area of the
circle?
Please can anyone show/explain to me the required calculations and the answer to each of the above?
 
1. I have an equilateral triangle in a circle and each of the points of the triangle are touching the circle. The inner circle area is 1891.59sq mtrs. How long is each side of the triangle?
When you wrote "The inner circle area", you were thinking "The circle's area", yes? In other words, there's no inner circle.

The value 1891.59 must have been rounded. Did you determine it, or was it given to you?

My first thoughts are: draw a picture, determine the circle's radius, pick a variable for the triangle's side lengths, label the known angles.

Have you learned the relationship between an inscribed angle and a central angle, when they each subtend the same arclength? Using this relationship, we could form a right triangle with:

1) adjacent side equal to half the equilateral triangle's side length;

2) hypotenuse equal to the circle's radius;

3) angle between the adjacent side and the hypotenuse equal to a special angle memorized from trigonometry.

Please show your work, so far (even if you're not sure it's correct).

Also, kindly read the forum guidelines. :cool:
 
2. I have an equilateral triangle inside a circle with each triangle side measuring 51.89mtrs, each point of the triangle touches the circle. What is the area of the circle?
Draw the circle and the triangle. Mark the (shared) center point; label this as A.

Draw a line from the center to one of the points of the triangle, where it touches the circle; label this as B. Draw another line from the center to the midpoint of an adjacent side of the triangle; label this as C. This will complete a smaller triangle. What can you say about this triangle? How can you solve this triangle? What value do you get for the length of AB? What does this say about the circle's area?

Please be complete. Thank you! ;)
 
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