Question

Which triangle shows the incenter at point A?

Point A is inside of a triangle. Lines are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle to cut each side into 2 equal parts.

Point A is inside of a triangle. Lines are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle. All angles have different measures.

Point A is inside of a triangle. Lines are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles.

Point A is inside of a triangle. Lines are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and to cut each side into 2 equal parts.

Answer 1

The third description.

Reason: the incenter is the intersection of the angle bisectors and is the center of the inscribed circle, so its perpendiculars to the three sides meet the sides at right angles (and those perpendicular distances are equal). Options 1 and 4 describe perpendiculars that hit side midpoints (perpendicular bisectors) — that is the circumcenter, not the incenter. Option 2 gives no perpendicular/angle-bisector property, so it doesn't identify the incenter.