Constructions — Part 2: Circumcircle, incircle and the regular hexagon: visual lesson, ICSE Class 10 Mathematics

Lesson

Circles of a triangle and a hexagon

Every triangle has a circle through its three corners, the circumcircle, and a circle touching its three sides, the incircle. A regular hexagon has both too.

In this lesson you will

Construct the circumcircle of a triangle and say where its centre lies for acute, right and obtuse triangles
Construct the incircle of a triangle and measure its radius
Construct a regular hexagon and draw its circumcircle and incircle
Calculate and check the radii against the measured values

Equilateral triangle: the perpendicular bisectors meet at the centre $O$. Lengths in cm.

Concept

What you will be able to do

Construct the circumcircle with perpendicular bisectors
Construct the incircle with angle bisectors
Say where the circumcentre lies for each kind of triangle
Construct a regular hexagon with its two circles

Concept

The circumcircle

The perpendicular bisectors of the three sides meet at one point, the circumcentre $O$ . It is equally far from the three corners, so the circle with centre $O$ and radius $OA$ passes through $A$ , $B$ and $C$ .

OA = OB = OC = R

Circumcircle: the perpendicular bisectors of the sides meet at $O$, and $OA = OB = OC$. Lengths in cm.

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