In the figure below, G is the center of the circle, LK is a diameter

In the figure below, G is the center of the circle, LK is a diameter, H lies on the circle, J lies outside the circle on LK, and JM is tangent to the circle at M. Which of the following angles or minor arcs has the greatest degree measure?

  1. arc LM
  2. arc MK
  3. ∠JMG
  4. ∠LHK
  5. ∠MJL

Answer

The correct answer is A.

Because measure of LM > ° 90 and measure of MK, ∠JMG, ∠LHK, ∠MJL are all less than or equal to 90°, arc LM has the greatest degree measure.

The tangent to a circle is always perpendicular to the radius drawn to the point of tangency. Because ΔMGJ is a right triangle
with right angle ∠JMG, the other angles in the triangle, ∠MJG and ∠MGJ, are acute.