Question

Drag and drop to complete the proof below:
Given: DE is tangent to circle C, at point F
Prove: E
D
F
חד
C

Answer 1

The proof of the given statements is shown below:

What is tangent to a circle?

A line segment which touches a circle specified to only one point is called a tangent to that circle.

1. given

2. A line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

3. Since the tangent is perpendicular to radius i.e., EFC is right angle then,

   angle EFC =90

4.  Sum of interior angles of a triangle is 180°.

5. proved above: angle EFC= 90

6. FEC + ECF= 180-90=90

7. As proved above

  FEC + ECF=90, its shows that angle FEC and ECF are complementary angle.

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