Final answer:
An inscribed circle in an isosceles triangle is centered on the triangle's angle bisector, is equidistant from the sides, and touches the sides at tangency points. To construct such a triangle over the inscribed circle, points of tangency to the circle are joined.
Step-by-step explanation:
A circle inscribed in an isosceles triangle is a circle that perfectly fits within the triangle, touching each of the triangle's sides at exactly one point. The characteristics of such a circle include:
- The circle's center is located on the angle bisector of the triangle's vertex angle.
- This center is also equidistant from the sides of the triangle, meaning it lies on the incenter of the triangle.
- The radius of the inscribed circle can be determined by the area and the semi-perimeter of the triangle (the inradius).
- Each point where the circle touches the triangle's sides is called a point of tangency, and these points form a tangent with the circle.
Furthermore, the isosceles triangle could be constructed using the circle by joining the points where the circle is tangent to the triangle's sides.