Γ is a circle with chord AB. P is a point outside of Γ such that PA is tangent to Γ and ∠BPA=90∘. If AB=48 and PB=8, what is the radius of Γ?
The angle between a tangent and the chord equals the angle subtended by that chord
Let angle BAP = Ø
sinØ = 8/48 = 1/6
then cosØ = √35/6
the central angle will be 2Ø
draw a perpendicular from the centre to the midpoint of AB, label it C, centre is O
consider triangle AOC , OA is the radius, r
AC = 24 , and angle AOC = Ø
sinØ = 24/r
r = 24/sinØ = 24/(1/6) = 144