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The centre of a circle inscribed in (touching the two sides meeting at) a triangle's vertex lies on the:
Answer & Solution
Correct answer: A.
1. A circle touching the two sides meeting at a vertex must have its centre equidistant from both sides.
2. The locus of points equidistant from two intersecting lines is the bisector of the angle between them.
3. So the centre lies on the angle bisector at that vertex.
4. Medians and altitudes do not, in general, contain points equidistant from both sides.
5. The perpendicular bisector of the opposite side is concurrent with the circumcentre, not the incircle.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._
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