1
$\begingroup$

I have a sector and would like a formula that gives the intersection between the bisector and the arc. here's a graph of the situation:

sector with bisector

the point B is the center of a circle of radius AB and the BD ray is the bisector of the ABC angle, knowing the coordinates of A, B, C as well as the ABC angle and the AB length I would like to know how I could calculate the coordinate of the D point. thanks by advance for your help.

$\endgroup$
  • $\begingroup$ It would help if you told us what did you try to solve this problem. $\endgroup$ – Moishe Kohan Aug 25 '14 at 20:49
  • $\begingroup$ I try to put labels at the exterior of the circle for each slices of a pie chart. the coordinate of D would be calculated for each slices and be used for putting the corresponding label there. $\endgroup$ – Graou13 Aug 25 '14 at 20:54
1
$\begingroup$

Find the midpoint $E$ of $AC$, then take $\lambda$ as $\frac{AB}{BE}$.

You will have $$ D = B + \lambda(E-B). $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.