Feb 23 - Law of Sine

Today, we will be looking further at the triangle and its circumscribing circle (CC), by investigating the relationship between the side lengths of the triangle and the diameter of its CC. This will lead to one of the central theorem about triangles, namely, the law of Sine.

A classical proof of the Law of Sine is outlined below.

For triangle ABC, construct its CC as shown in the diagram.
Draw line from B through the center of the CC to intersect CC at point T. Length of TB is 2R (the diameter of the CC). Angle TCB is a right angle, by Thale's theorem.

Since We have

By drawing diameters from point A and C, we can similarly prove

Combined into a simpler form, the Law of Sine is usually written as

Feb 16

Welcome back.

Today, we'll look at

1. the relational properties of lines and circles, as in tangents and secants. and time permits, start to go over

2. the relational properties between circles and circles.

Assignments

(AMC10 2008) A round table has radius 4. Six rectangular place mats are placed on the table. Each place mat has width 1 and length x. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length x. Further, the mats are positioned so that the inner corners each touch an inner corner of an inner corner of an adjacent mat. Find x.

(AIME 2005) Six congruent circles from a ring with each circle externally tangent to the two circles adjacent to it. All six circles are internally tangent to a circle C with radius 30. Let K be the area of the region inside C and outside all of the six circles in the ring. Find K.

No Class Feb 9

Please remember we have no class today, in observance of the Chinese New Year.

Richard Feynman

Richard Feynman interview

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RACL Math Class Notes - Feb 09

First Class - Assessment  
Assignment: Pythagorean Theorem Proof

2nd Class - Circles
Assignment: Thales Theorem Proof