The solution of this question will make use of the Two Tangents from Point Theorem which states that "the measure of an angle formed by two tangents drawn from a point outside the circle is half the the difference of the intercepted arcs".
We can also see that the measure of arcs are: and
Thus, as per the theorem, the measure of the can be calculated as:
Therefore, we get:
Thus, out of the given options, option B is the correct option.
The Length of FD = 26 cm
According to the given information
FE = FC = 12cm
As FE, FC both are radius of circle
The tangent segments to a circle from a external point are equal
Hence
CD = ED
13x - 16 = 4x + 11
13x - 4x = 11 + 16
9x = 27
x = 27/9
x = 3
CD = 13x - 16
= 13 × 3 - 16
= 23 cm
ED = 4x + 11
= 4 × 3 + 11
= 23 cm
In Triangle FED
FE is perpendicular to ED
According to Pythagoras Theorem
=
= 673
FD = 26 cm approx.
The Length of FD = 26 cm
To know more about Pythagoras Theorem
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