Question

Prove: AD is tangent to circle C.

a) Circle C is constructed so that CD=DE=AD.
b) AD is a radius of circle C.
c) △ACD is an isosceles triangle; △ADE is an isosceles triangle.
d) All of the above

Answer 1

To prove that AD is tangent to circle C, we can apply the given information about the circle and the triangles to show that AD is a radius and perpendicular to the tangent line. Hence the correct answer is option D

Step-by-step explanation:

To prove that AD is tangent to circle C, we need to use the given information:

1. Circle C is constructed so that CD=DE=AD.
2. AD is a radius of circle C.
3. △ACD is an isosceles triangle; △ADE is an isosceles triangle.

From the second statement, we know that AD is a radius of circle C, so it is perpendicular to the tangent line at point A. Therefore, AD is tangent to circle C. Hence, the correct answer is (d) All of the above.