Break out your compass, ruler and colorful pens. Here's the cliff notes version of constructing a 9 point circle by hand. 1.Draw a scalene triangle and construct midpoints. These are done by putting the sharp end of the compass on a vertex and extending the pencil slightly more than half the estimated distance along that segment of the triangle. Draw an arc and do it the same from the other end of the segment. Repeat for the other two sides. 2. Draw altitudes. Put sharp end of compass at a ver...

Graphing polynomials begins with finding the x-intercepts, or roots, of the function. Take y=(x+1)(x-2)². First set y= to zero and find what values for x satisfies that. If either term equals zero, we know that the product of the two terms will equal zero. So if x=-1 or x=2, y will equal zero. We now can sketch the x-intercepts. Now, let's think about end behavior of the polynomial. Since it is a third degree polynomial (the parent function is x^3), we know that as x becomes more and more negati...

In the following question we are asked to find angle Y in the pictured circle. We are given angle E as 80° and told that the rays extending from point E are circumscribed to circle O (they are tangents to the circle). In order to find angle B we first must recall that angles F and G will be 90° because any radius segment will meet perpendicular to a tangent line. And if you recall that a quadrilateral has 360°, we know that angle O will be 100°. Since angle O is a central angle, it is als...

A common question in geometry class is finding inscribed angle. What is an inscribed angle? It's an angle formed by two chords that have a vertex at one edge of a circle and distinct endpoints at somewhere else on the circle. This is in contrast to a central angle, which has a vertex at the center of the circle, from which two legs extend to the edges of the circle. In the picture above of problem 1, we see the top circle consists of a central angle that forms an arc of 90 degrees. Below ...

Imagine you're on a boat in the ocean and in the far distance a sliver of land appears. You wonder: How can we calculate that distance between us and that piece of land. The distance depends on two things: the curvature of the earth (a known entity) and the height of your eyes from the water's surface. We can use height above the surface in feet and distance to horizon in miles. Let's use the equation: sqrt(height above surface/0.5736)= distance to the horizon. Let's look at a 100 ft tall ...