Question

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

Answer 1

Answer:

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.

Answer 2

3)AD = CD = The radius o the circle. 
AD = DE = The radius o the greatest circle. 
4)The sum of the angles of any triangle equate is 180 degrees. 
5)Measure DCA = Measure CAD, Measure DAE = Measure AED.
9)Statment 8.