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; CA is a radius of circle C.

Prove: AE is tangent to circle C.

Step 3 Reason: If in a triangle two sides are equal, then it is an Isosceles Triangle.

Step 4 Reason: The Sum of interior angles of Triangle is 180°.

Statement of Step 5: Isosceles Triangle Theorem states that ,the two equal sides of Isosceles triangle have equal opposite angles.

Reason for step 9: Addition Subtraction Property

Reason for step 10: ∠ADC and ∠EDA, lie on a straight line,CE.Also, AD is a ray,through point D.

Statement for Step 11: Linear pair Postulate states that,the two angles which are adjacent of a common ray on a line have the sum 180°.

Reason for step 16: Dividing both sides by -2.

Statement for step 18: ∵ m∠CAE=90°

Statement for step 20: CA ⊥ AE

Reason for step 21: If the angle between radius and the point of contact of a line or line segment which  passes through the end of segment of  radius which lies on circle is of 90°, then that line is tangent to the circle.