Question

1. choose the correct answer.

which triangle illustrates an incenter?

Explanation:

The in - center of a triangle is the point of intersection of the angle bisectors of the triangle. In option B, the lines are angle bisectors (marked with angle - equal signs), and the in - center is equidistant from all the sides of the triangle (represented by \(XP = YP=ZP\)).

• Option A shows the centroid (since \(AP=\frac{2}{3}AZ\), \(BP = \frac{2}{3}BX\), \(CP=\frac{2}{3}CY\), centroid divides the medians in the ratio \(2:1\)).
• Option C shows the ortho - center (as there are perpendicular lines from vertices to the opposite sides).
• Option D shows the circum - center (if \(AP = BP=CP\), the point is equidistant from the vertices).

Answer:

B