External tangents

Two circles have radius of 4cm. and 12cm. respectively. If the distance between their centers is 30cm., compute the length of the common external tangent to the two circles on one side only.
It says the answer is 31.05cm.

The following image is my solution but as you can see i got 28.914cm. Please help me. I cant seem to find where did i make a mistake. Thanks a ton sir!

Good day po sir! Is the angle of intersection between two chords of a circle equal to one of the vertical angles of the cyclic quadrilateral that is formed by this chords? Im so confused. Please help. Below is the problem followed with my progression. Thanks a ton!