A) 5.5 units
b) 10.9 units
c) 5.0 units
d) 8.5

Since diameter is always perpendicular to tangent at point of contact in circle,

in this case:

AC is perpendicular to BC

which makes triangle ABC right angled triangle,

So from Pythagoras theorem,

AC=√(AB²-BC²)

=√(12²-5²)

=√(144-25)

=√119

=10.9

Since radius is half the length of diameter:

AP= AC/2

=10.9/2

=5.45 (nearly equal to 5.5)