![]() ![]() Is using some of the results of the last few videos and a So from the center to theĬircumference at any point, this distance, the ![]() Then this is side length a, and that is also a That means all of these sides are the same length. So I'm going to try my best toĭraw an equilateral triangle. This triangle sit on the circumference of the circle. So let's say this is a circle,Īnd I have an inscribed equilateral triangle Is use some of the results from the last several videos toĭo some pretty neat things. So when you take off the circle the area is 144 * SQRT(3) - 48 pi Using Heron's formula the area is 24^2 * SQRT(3)/4ġ7. So the area of the circle is 48 pi you need to find the area of the equilateral triangle.ġ5. The area of the circle is (4 * SQRT(3)^2 * pi which is also 48 piġ4. If you rationalize the fraction you get r = 12 * SQRT(3) / 3ġ3. Half the base of the equilateral triangle is 12. If you drew the 30-60-90 triangle on the base of the equilateral triangle you can see the longer leg of the 30-60-90 triangle is the same as half the base of the equilateral triangle. This cuts the equilateral triangle in half.ĩ. Now draw the height of the equilateral triangle. So you know the longer leg is r * SQRT(3)Ĩ. The radii you drew is the short side of the triangle you created.ħ. This a 30 - 60 - 90 triangle because you bisected one of the original angles of the equilateral triangleĦ. (For simplicity draw the line segments to the base, so connect the radii you are drawing to the base of the triangle where it is being touched by the circumference of the circle)ĥ. ![]() Connect another line segment to an apex of the same side. Connect a radii to any part of the circumference of the circle that is touching the triangle.ģ. Draw the figure and label the sides of the equilateral triangle in this case 24.Ģ. You can now use the formulas shown in the video for the area of the triangle and the circle.Īrea = (SQRT(3)*x^2) / 4 - pi * R^2. Just like the example in the video, the distance from the center to the outside triangle apex is 2*R, and the distance of the distance of the base of the inside triangle is SQRT(3) R, and by definition that distance is x/2 (half the length of the outside triangle edge). You know this because the equilateral triangle angle was 60 degrees, and you just bisected it. This forms a right angle with that line, and that length = R (radius).Īlso draw a line from the center to a nearby apex of the triangle (on the same triangle line edge). This is a bit more challenging to do without video, but if you understood the video, you could probably follow:ĭraw the figure (outside equilateral triangle with inscribed circle).ĭraw a line from the center of the circle to a point where the circle barely touches the triangle. Let's take the example that you know the radius of the (inside) circle. or the radius of the (inside) circle, you can figure out the other. For example, if you know either the length of the (outside) equilateral triangle. ![]()
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