G is a circle with chord AB. P is a point outside of G such that PA is tangent to G and ?BPA=90°. If AB=48 and PB=8, what is the radius of G?
The angle between a tangent and the chord at their point of contact is equal to half the angle at the centre.
So once we find angle BAP it should not be that bad
In right-angled triangle ABP , P = 90°
let angle BAP = Ø
sinØ = 8/48 = 1/6
Ø = 80.4°
so 2Ø or central angle = 160.8
In triangle AOB , where O is the centre, and OA = OB = radius
angle OBA = 9.59°
by the sine law:
OB/sin9.59° = 48/sin160.8°
OB = 24.3
The radius is 24.3 units