The incircle of a triangle is tangent to which features?

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Multiple Choice

The incircle of a triangle is tangent to which features?

The essential idea is the inscribed circle, or incircle, of a triangle. An incircle sits inside the triangle and is tangent to each of the triangle’s three sides. “Tangent” means the circle just touches a side at exactly one point, so there are three touch points—one on each side. This circle’s center is where the angle bisectors meet (the incenter), and the common distance from the center to all three sides is the radius. Because it is defined to touch every side, the incircle is tangent to all three sides. It isn’t, in general, tangent to the circumcircle, which is a different circle that passes through the triangle’s vertices.

The essential idea is the inscribed circle, or incircle, of a triangle. An incircle sits inside the triangle and is tangent to each of the triangle’s three sides. “Tangent” means the circle just touches a side at exactly one point, so there are three touch points—one on each side. This circle’s center is where the angle bisectors meet (the incenter), and the common distance from the center to all three sides is the radius. Because it is defined to touch every side, the incircle is tangent to all three sides. It isn’t, in general, tangent to the circumcircle, which is a different circle that passes through the triangle’s vertices.

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