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Tuesday, December 06, 2005

Scribe Scribles

Today in class, Mr. K. put us into groups to work on some problem solving sheets for circles. Sorry if some of this is wrong, feel free to correct me in the comments. (=

Problem Solving Circle 1:













Given:
- DC and DE are tangents to the circle at points C and E respectively
- F is the centre
- AE is a diameter


Prove: L1 = L2












This picture shows:
- Tangent-radius theorem
- ΔCFE is isosceles
- ΔCDE is isosceles

a + b = 90°
L1 = 2b
2a + L2 = 180°
a = 90° - b

2(90° - b) + L2 = 180°
180° -2b + L2 = 180°
-2b + L2 = 0
L2 = 2b


Problem Solving Circle 2:











Given:
- AE is tangent to the circle at A
- CE is perpendicular to AE
- CD is perpendicular to AB
- AC = BC

Prove:
- CE = CD












This picture shows:
- L2 = L6 tangent-chord theorem
- ΔABC is isosceles, L3 = L6
- ΔADC = ΔAEC by AAS
- DC is congruent to EC
Q.E.D. (added that in just to make Mr. K smile)

Problem Solving Circle 3:












Given:
- AB is a tangent
- BD = CD
- AB = BC

Prove:
- L3 = L6












This picture shows:

- ΔBCD is isosceles
- L4 = L5 + L7
- L2 = L5 + L7, by tangent-chord theorem
- L4 = L2
- ΔABC is isosceles
- L1 + L5
- L3 + L6

*Bell rings, and we're out of time folks!

The next scribe is... abriel_S. (=

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