Posted by **abc Please help URGENT** on Saturday, May 4, 2013 at 2:59am.

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?

- Math -
**Reiny**, Saturday, May 4, 2013 at 8:09am
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

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