Geometry Help /
I need some help on a few geometry questions.
1. If a median is drawn to any side of a scalene triangle, the two triangles formed will have the same area. Always,Sometimes, or Never.
2. A right triangle is circumscribed about a circle with sides 16,30,34. Find the radius of the circle.
3. Two circles have radii of 11 and 4, from radius to radius they are 13 units apart. Find the external tangent.
May 22, 2013
4 Comments • Newest first
1. I'm not sure, but I'm positive that the answer is either sometimes or always. I tested the theory on a 30-60-90 right triangle, and it worked. But if this was some kind of bet, I'd put my money on always.
[url=http://img534.imageshack.us/img534/7186/69784683.png]2. Easiest of them all.[/url]
[url=http://img7.imageshack.us/img7/596/39752929.png]3. Labeled it, easy to understand. You should be able to do it now.[/url]
These are pretty simple questions so I'm not going to just spoon feed you the answer lol
1. Think of it this way. The median goes from one vertex, through the center of the triangle, to the midpoint of the opposing side. This splits the triangle right down the middle.
2. Circumscribed right triangle R = c/2 R being the radius. C being the hypotenuse.
3. Okay you have Circle 1 (C1) with a radius of 11 (R1) and Circle 2 (C2) with a radius of 4 (R2). The distance (D) between the center of each circle is 13. So it helps if you draw this out (preferably with the radius of each circle pointing up to make it even easier). The measurements don't have to be exact, but the first circle should be bigger than the second. What you're trying to find is the line that goes from the top of C1 to the top of C2.
First to make this easier, make a smaller circle inside of C1 that has a radius of R1 - R2, we'll call this Circle 3 (C3) and it's radius R3. No draw a tangent line from the top of C3 to the center of C2. This line, we'll call it F, should be parallel with the external tangent (it forms a quadrilateral) that you're trying to find. Line F is also equal to the tangent you're tying to find and forms a right triangle with R3 and D. So since you already know the length of two of the sides you solve using the Pythagorean theorem.
d^2 = f^2 + r^2 ---> f = sqrt(d^2 - r^2) r in the equation being R3. So once you find F you'll have the answer for the external tangent. Yes, that's right, you still have to do all the math part yourself lol.
You gotta pay us before we do the questions.
help pls :C