Answer:
The radius of circle O is 13
LP is a diameter of circle O.
∠LMP intercepts a semicircle.
Step-by-step explanation:
The missing image is attached in the diagram below.
From the diagram;
we can determine the length LP by using the Pythagoras theorem.
i.e.
hypotenuse² = opposite² + adjacent²
LP² = ML² + MP²
LP² = 24² + 10²
LP² = 576 + 100
LP = [tex]\sqrt{676}[/tex]
LP = 26
Since line LP cuts the circle into two equal halves, we can say the line LP is the diameter of circle O.
if the diameter (LP) = 26
Then, the radius r = 26/2 = 13
The radius of circle O is 13.
Similarly, the arc LMP is 180° (∵ inscribed angle is 1/2 the measure of central angle), and LMP is 180°, then ∠LMP intercepts a semicircle.
