B) The construction of a tangent to a circle given a point outside the circle can be justified using the second corollary to the inscribed angle theorem. An alternative proof of this construction is shown
below. Complete the proof. (5 points)
Given: Circle C is constructed so that CD = DE = AD; is a radius of circle C.
Prove: is tangent to circle C.
ADCE
Reasons
Statements
1.
Circle C is constructed so that CD = DE = AD;
Given
is a radius of circle C.
Definition of congruence
2.
CD=AD
3.
3.
ACD is an isosceles triangle;
ADE is an isosceles triangle.
4
5.
Isosceles triangle theorem
5.
6.
Definition of congruence
6.
:
7
Substitution property
7.
:
8.
Addition
18
9.
i
M