To complete steps 5 - 6 of the proof, refer to the diagram shown below.
Because OL = OM = ON = the radius, therefore each of ΔOLM and ΔONM is an isosceles triangle.
ΔOLM has two equal angles denoted by a, and ΔONM has two equal angles denoted by b.
The central angles x and y add up to 180° on a straight line, so
x + y = 180 (1)
Because angles in a triangle sum to 180°, therefore
x + 2a = 180 (2)
y + 2b = 180 (3)
Add (2) and (3) to obtain
x + y + 2(a + b) = 360
From (1), obtain
180 + 2(a + b) = 360
2(a + b) = 180
a + b = 90
Answer:
Because (a + b) = ∠LMN, it proves that ∠LMN = 90°
