Answer:
r = 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
the radius r of the circle is AB
the angle between a tangent and the radius at the point of contact = 90°
then Δ Abc is a right triangle
using Pythagoras' identity
AB² + BC² = AC² ( substitute values )
AB² + 5² = 7²
AB² + 25 = 49 ( subtract 25 from both sides )
AB² = 24 ( take square root of both sides )
AB = [tex]\sqrt{24}[/tex] = [tex]\sqrt{4(6)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] = 2[tex]\sqrt{6}[/tex]
