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

Answer:

50 degrees

Step-by-step 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

$\sin E=\dfrac{8.5}{20} \\\angle E=\arcsin \dfrac{8.5}{20}\\\\\angle E=25^\circ (to the nearest degree)$

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)