Inscribed CircleDate: 18 Mar 1995 14:09:31 -0500 From: Anonymous Subject: formula for the area of an inscribed circle in an equilateral triangle I need the formula to find the radius of an inscribed circle in an equillateral triangle. I also need to know the rationalization for the method. Date: Sun, 19 Mar 1995 10:19:16 +0000 From: Dr. Math Subject: Re: formula for the area of an inscribed circle in an equilateral triangle Hello there! Here's one way to figure out how long the radius in question is: let's say we have an equilateral triangle, and each side has length s. Then find the center of the triangle. You can do this by drawing the three altitudes, or the three medians; in this case, they're all the same lines. Then draw the segment that starts at the center of the triangle and ends at the midpoint of one of the sides. This is the radius of the inscribed circle. To find out how long it is, notice the following: Let's say our triangle has vertices X, Y, Z, and let's call the center of the triangle C, and the midpoint of one of the sides M. Then look at triangle XCM. Since each angle in an equilateral triangle is 60 degrees, how big is angle MXC? So, is this a special kind of triangle (Hint: yes!!)? So, if it has its longer leg with length s/2, you can use that information to find the length of its shorter leg. Let us know if you're still stuck! -Ken "Dr." Math |
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