Question

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

Answer 1

1.44

2.74

3.13,464 miles

4.3.5 ft

5.9.2

6.56 degrees

7.69.5 degrees

8.84

Explanation:

Answer 2

The quadrilateral is cyclic, because the angle that the tangent and the radius meet forms a right angle. Since the two opposite angles are 90° each, they form a 180° summation. Thus, the four points are cyclic.

Now, the smaller ∠O is 135, which means x is 180 - 135 because the four points are concyclic. Thus ∠O + x = 180°
Hence, x = 180 - 135 = 45°

∴ x = 45°