9A Class- 4/13/2009

In todays class, Mrs. Saatkamp explained Theorems: 9-14, 9-15, and 9-16. She also gave us some new terminologies to use, which were explained by using the diagram from 9-15.

Theorem 9-14: If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.

In this diagram, "A" is the center of the circle. So, the theorem uses the word product, which means the result of a multiplication.

The formula presented by this Theorem is:

----------/------------/------------/----------/-------------/-------------/------------/-------

Theorem 9-15: If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

In this diagram, the center of the circle is "A", the external point is "C". The terminologies defined by Mrs. Saatkamp with this diagram were:

CD and CE = Secant Segments
GD and FE = Chords
CG and CF = External Secant Segments\Exterior Secant Segments

Th actual formula presented by this Theorem is (the formula is relevant to the diagram above):

-----------------\-----------------------\--------------------------\--------------------\------

Theorem 9-16: If a tangent segment and a secant segment are drawn to a circle from an exterior poin, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

The formula presented by this Theorem is:

After Mrs. Saatkamp finished explaining everything, she revised the quadratic formula, whish will be needed in the homework in questions which have both an x^2 and an x in them. When the exercise is already formatted for the quadratic formula, it should look like this: