Angle Bisectors and Incircle
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(0:01) What is an Angle Bisector?: A line or ray that divides an angle into two equal parts. For example, if the angle is $60^\circ$, the angle bisector will split it into two angles of $30^\circ$ each.(0:40) How to Construct Angle Bisectors with a Compass?: Draw an arc from the vertex to create intersection points. Then, without changing the compass width, draw additional arcs from each point. Finally, draw a straight line connecting the vertex to the intersection of these arcs to form the angle bisector.(1:14) Key Property of Angle Bisectors: Every point on the angle bisector is the same distance from both sides of the angle.(1:26) How to Find the Incenter of a Triangle?: The incenter is the point where the three angle bisectors of a triangle meet. To find it, draw the angle bisector of each vertex. The point where all three bisectors intersect is the incenter, which is the same distance from each side of the triangle.(1:50) What are Inradius and Incircle?: The inradius is the perpendicular distance from the incenter to any side of the triangle. The incircle is a circle centered at the incenter with a radius equal to the inradius, touching all three sides of the triangle.
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