I am trying to solve a multiple choice geometry problem that involves finding the area of a kite that is inscribed in a circle. The problem is given below:
Consider a circle with centre $O$ and a $1$ cm-long radius. Let $P$ be a point outsid this circle. The tangent lines from $P$ to the circle meetthe circumference in two points $A$ and $B$. We know that the area of $PAOB$ is equal to $\sqrt3$ cm2. What is the distance between $P$ and $O$.
A. $3$ cm
B. $2$ cm
C. $4$ cm
D. $\frac{\sqrt3}2$ cm
E. $\frac32$ cm
I have drawn a figure of the problem, which is also shown below:
I know that I can use the formula for the area of a kite, which is $A = (d_1 * d_2) / 2$, where $d_1$ and $d_2$ are the lengths of the diagonals. However, I don’t know how to find the length of $AB$, which is one of the diagonals. Can anyone help me with this step?
You are right making a drawing of the exercise.
But the drawing you have made is horribly wrong: it looks like the angle in $o$ is a right-angle, while the ones in $A$ and $B$ are not, while it's just the opposite.
This would be a better drawing of the whole situation (the distances are wrong, but the right-angles are on the right place):