# Solution to the Angles in Two Circles Puzzle +-- {.image} [[AnglesinTwoCircles.png:pic]] > What's the sum of the two marked angles? =-- ## Solution by the [[Alternate Segment Theorem]] and [[Angles in a Triangle]] +-- {.image} [[AnglesinTwoCirclesLabelled.png:pic]] =-- With the points labelled as above, the [[alternate segment theorem]] gives that both angles $C \hat{B} D$ and $B \hat{C} D$ are both $a$ while $C \hat{A} D$ and $D \hat{C} A$ are both $b$. As [[angles in a triangle]] add up to $180^\circ$, considering triangle $A B C$ shows that $a + a + b + b = 180^\circ$, and so $a + b = 90^\circ$.