Check the picture below.
since chords NQ and MP cross the center of the circle at R, that means that those two chords are diametrical chords and the angles made by both are vertical angles and thus twin angles, namely both are 18° as you see in the picture, so the angle NMP in magenta is really 162° + 18° + 18° = 198°, and we know the radius NR is 8.
Answer:
Step-by-step explanation:
If AB is tangent to the circle, then angle ABO is right angle and triangle AOB is special triangle. In this triangle, the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,
By the Pythagorean theorem,
Make use of the known limit,
We have
since , and the limit of a product is the same as the product of limits.
is continuous at
, and
. The remaining limit is also 1, since
so the overall limit is 1.
