Question

C. Write the formula for finding the measure of the inside angle formed by two chords.



D. Show your calculations and find the length of FD if is the diameter of circle C.

Answer 1

The equation of a circle is \[(x-h)^{2}+(y-k)^{2}=r^2\]Given that the center of the circle is (0,0) the equation now becomes\[(x-0)^{2}+(y-0)^{2}=r ^{2}\]

Answer 2

So now you need to find the value of r

To find the value of r, first find the value of the diameter. The diameter is DF + FE.
FE is given as 2cm. So we need find the value of DF.

To find DF, we reference the theorem that states: If two cords intersect in a circle, then the
products of the measures of the segments of the cords are equal.

The measures of cord AB are AF= 8cm and FB = 3cm. The measures of cord DE are FE = 2cm and DF = x.

So the products of the measures of the segments are:

(x)(2)=(8)(3)
x=12cm So DF = 12cm

Now we can find the diameter by adding DF + FE

12cm + 2cm = 14 cm

The radius is 1/2 the diameter.

So the radius = 7cm

So equation of the circle is:\[x ^{2}+y ^{2}=49\]