Final answer:
To prove KN=EN, we use the property of congruent triangles. MNA is a tangent to circle KEN because the angle between a tangent and a radius of a circle is 90 degrees. KL=LG can be proven using the property of congruent triangles.
Step-by-step explanation:
To prove that KN=EN, we can use the property of congruent triangles. Since triangles MNA and MNE share the side MN and have a common angle at M, they are congruent by the Side-Angle-Side (SAS) congruence criterion. Therefore, KN must be equal to EN.
To prove that MNA is a tangent to circle KEN, we can show that the angle between a tangent and a radius of a circle is 90 degrees. Since MNA is a line that passes through the center of the circle KEN and touches it at point N, angle MNA must be 90 degrees, making MNA a tangent.
To prove that KL=LG, we can use the property of congruent triangles again. Since triangles KFL and KLG share side KL and have a common angle at K, they are congruent by the Side-Angle-Side (SAS) congruence criterion. Therefore, KL must be equal to LG.