Question

diameter eg is drawn on circle h and point f is located on the circle such that gf = 8.5 inches. if the radius of the circle is equal to 10 inches , then what is the measure of gf to the nearest degree

Answer 1

50 degrees

Explanation:

Theorem: The angle subtended by the diameter is a right angle.

By the Circle Theorem above, the angle at F is a right angle and thus Triangle EGF is a Right Triangle.

We are to determine the measure of GF.

|GE|=|GO|+|OE|=10+10=20 Inch

Using Trigonometry in the second triangle attached

`\sin E=(8.5)/(20) \\\angle E=\arcsin (8.5)/(20)\\\\\angle E=25^\circ$ (to the nearest degree)`

Theorem: Angle at the centre is twice the angle at the circumference.

By the theorem above:

Measure of Arc GF = 2 X
`\angle FEG`

=2 X 25

mGF=50 degrees

Therefore, the measure of GF is 50 degrees (to the nearest degree)