The radius of the circle is 17 units
Circle theorem
A radius is defined as the distance from the centre to the circumference of a circle.
From the given diagram,
AQ = QB
Given the following parameters
AQ = 4x + 3
QB = 7x - 6
Substitute
4x + 3 = 7x - 6
4x - 7x = -6 - 3
-3x = -9
x = 3
Determine the measure of AQ
AQ = 4x + 3
AQ = 4(3) + 3
AQ = 15
Using the Pythagoras theorem;
QE² = AE² + AQ²
QE² = (16/2)² + 15²
QE² = 8² + 15²
QE² = 64 + 225
QE² = 289
QE = 17 units
Hence the radius of the circle is 17 units
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