Answer:
radius = 40
Step-by-step explanation:
From the diagram the radius PQ = x
Since PR is a tangent to the circle then the angle between the tangent and the radius at the point of contact is 90°
Thus Δ PQR is a right triangle
Using Pythagoras' theorem in the right triangle
(x + 18)² = x² + 42² ← expand factor on left side using FOIL
x² + 36x + 324 = x² + 1764 ( subtract x² from both sides )
36x + 324 = 1764 ( subtract 324 from both sides )
36x = 1440 ( divide both sides by 36 )
x = 40
The radius of the circle is 40
