Question

Solve for y to the nearest tenth.

Answer 1

From the figure it is clear that O is the centre of the circle and OB and OC are its radii
so OC=OB=6

Answer 2

From the figure it is clear that O is the centre of the circle and OB, OA and OC are its radii
so OC=OB=OA=6
AP is tangent to the circle at A
so angle OAP = 90 degrees\
OP=OC+PC=6+5=11
therefore triangle OAP is a right angled triangle
so by Pythagoras theoprem
\[OP^2 =OA^2+AP^2 \]
\[11^2 =6^2+Y^2 \rightarrow Y^2 = 121 -36=85\]
\[Y^2 = 85 \rightarrow Y =\sqrt 85 \rightarrow Y=9.219\approx 9.2\]