GCSE Maths Practice: loci-and-constructions

Question 7 of 10

This question introduces the incenter of a triangle.

‹ ›

\( \begin{array}{l}\text{What is the point where the three angle bisectors of a triangle meet?}\end{array} \)

Choose one option:

Draw all three angle bisectors accurately; the intersection is the incenter.

The incenter is the point where all three angle bisectors of a triangle intersect. It is equidistant from all sides of the triangle, making it the center of the inscribed circle (incircle). Understanding the incenter is essential in geometric constructions, proofs, and triangle properties. Students should practise constructing angle bisectors using a ruler and compass and locating the incenter. Visual diagrams reinforce the concept of equidistance and symmetry. Mastering the incenter helps in solving problems related to incircles, triangle optimisation, and geometric loci. Regular practice ensures familiarity with construction techniques and enhances spatial reasoning.