more geometry questions?

Question

Prove that the tangents to a circle at the endpoints of a diameter are parallel.State what is given, what is to be proved, and your plan of proof. Then write a 2 column proof. Hint: It will help you to draw a diagram with the points labled.
Given:
To Prove:
Plan:

Answer 1

The first thing to do is to extract from this problem a list of the
"givens" (the things you are told are true).
So here's what we are given:

GIVEN - Segment AB is the diameter of a circle with center O
Line AC is tangent to circle O at A
Line BD is tangent to O at B

TO PROVE - AC and BD are parallel

STATEMENTS REASONS

1. Segment AB is a diamter of circle O Given
2. Line AC is tangent to O at A Given
3. Line BD is tangent to O at B Given

4. AC is perpendicular to AB Tangent line is perpen-
dicular to the radius

5. BD is perpendicular TO BA Theorem as stated in
#4 (Theorem 9-1 - If a
line is tangent to a
circle, then the line
is perpendicular to
the radius drawn to
the point of tangency)

6. AC is perpendicular to AB Two lines perpendicu-
lar to same line are
parallel (Theorem 3-7
In a plane two lines
perpendicular to the
same line are parallel





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