Task 636
Task 636: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In the figure, circle $O$ has radius 6 units. Chord $CD$ has length 8 units and is parallel to segment $KB$. If $KA$ = 12 units and points $K$, $A$, $O$ and $B$ are collinear, what is the area of…
The task
In the figure, circle $O$ has radius 6 units. Chord $CD$ has length 8 units and is parallel to segment $KB$. If $KA$ = 12 units and points $K$, $A$, $O$ and $B$ are collinear, what is the area of triangle $KDC$? Express your answer in simplest radical form. [asy] draw(Circle((0,0),6)); dot((0,0)); label("$O$",(0,0),S); label("$A$",(-6,0),SW); label("$B$",(6,0),SE); label("$K$",(-18,0),W); draw((-18,0)--(6,0)); label("$C$",(-4,sqrt(20)),NW); label("$D$",(4,sqrt(20)),NE); draw((-18,0)--(-4,sqrt(20))); draw((-18,0)--(4,sqrt(20))); draw((-4,sqrt(20))--(4,sqrt(20))); [/asy]