Learning Resources

Focus F: Proving Tangent Properties

Test yourself (solution)

In the diagram below, it is given that ED is a tangent to the circle at point C and AC @ BC. Prove that ED || AB

Proof:

1. ED is a tangent to the circle at point C (given)

2. Ð ECA @ Ð CBA (a tangent chord angle is equal to the inscribed angle on the opposite side of the chord.)

3. AC @ BC (given)

4. D ACB is isosceles (two sides equal)

5. Ð CBA @ Ð CAB (base angles of an isosceles triangle)

6 Ð ECA @ Ð CAB (substitution in steps 2 and 5)

7. ED || AB (alternate interior angles congruent)