+380 Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$
+307 Maybe its saying AP = 4? That sounds more reasonable
So this is a kite shape, and the kite is concyclic because opposite angles add to 180
Therefore, the area can be represented by \(\sqrt{(9-5)(9-5)(9-4)(9-4)}\)
which is \(20\)
The area can also be represented by the 2 diagonals divided by 2,
\(\frac{\sqrt{41}\cdot{x}}{2} = 20\)
\(x = \frac{40}{41}\cdot\sqrt{41}\)
+307 Maybe its saying AP = 4? That sounds more reasonable
So this is a kite shape, and the kite is concyclic because opposite angles add to 180
Therefore, the area can be represented by \(\sqrt{(9-5)(9-5)(9-4)(9-4)}\)
which is \(20\)
The area can also be represented by the 2 diagonals divided by 2,
\(\frac{\sqrt{41}\cdot{x}}{2} = 20\)
\(x = \frac{40}{41}\cdot\sqrt{41}\)
