Page 230 - ICSE Math 7

Circumcircle

A circle which passes through all the three vertices of a triangle is Maths Info
called the circumcircle of the triangle. The centre of the circumcircle Circumcentre of a triangle is
is called circumcentre and its radius is called circumradius. always equidistant from the
To construct the circumcircle of a triangle, follow the steps given below. three vertices.

Step 1: Construct the triangle with the given
measurements. A A

Step 2: Draw the perpendicular bisectors
of any two sides of the triangle, say
AB and BC. Let the perpendicular
bisectors intersect each other at O. O O
Step 3: With O as centre, draw a circle with B C B C
OA, OB or OC as radius. The circle
drawn will pass through all the three
vertices of DABC. Here, O is the
circumcentre and OA = OB = OC
is the circumradius.

Incircle

A circle drawn inside a triangle which touches all the three sides of the triangle is known as the incircle
of the triangle. The centre of the incircle is known as incentre. To construct the incentre of a triangle,
follow the steps given below.
A
Step 1: Construct the triangle with the given measurements.
Step 2: Draw the angle bisectors of any two angles of the triangle,
say ∠ABC and ∠ACB. Let the bisectors intersect each other O
at O. B C

A

Step 3: With O as centre, draw perpendicular on BC which intersects O
BC at D.
B D C

A

Step 4: With O as centre and OD as radius, draw a circle. The circle O
drawn will touch all the three sides of DABC. Here, O is the
incentre of DABC. B D C

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