In this lesson you will learn how to construct Midpoint of a Line Segment and Inscribe
a Circle in the given Triangle. It is explained by making use and of tools
for basic construction and their application to build skills for higher concepts.
The presentation covering such content will be done by the instructor in own handwriting,
using video and with the help of several examples with solution. (More text below video...)
(Continued from above) Constructing
the midpoint of a segment  simply saying means, for constructing the midpoint of
a line segment AB, you first draw the line segment and then draw arcs of the same
radius centered at A and B respectively using compass. Then join the intersection
points of the arcs i.e. C and D. Line CD bisects AB at point E, which is the midpoint
of the line segment AB
Given: line segment
Construct: Midpoint of
Procedure and steps of construction
 draw line segment
(Figure 1).
 use the compass centered at point A and the radius exceeding half the length
of AB. Draw two arc as shown in Figure 2.
 keeping radius the same, now center the compass at point B and draw two
arcs intersecting the earlier drawn arcs. Say these intersect at points P and Q
 use the straightedge to draw line PQ, that intersects AB at point M. Conclusion:
point M is the midpoint of line segment AB. Also line PQ is perpendicular to line
segment AB.
Construct a Circle in a given Triangle:
Given: A triangle
ABC
Construct: A circle inscribed in
ABC
Procedure and steps of construction:
 ABC is the given triangle (Figure 1).
 construct the bisectors ofA
and
B
(Recall the procedure for angle bisector construction). The two angle bisectors
intersect at Q (Figure 2).
 construct a line through point Q, perpendicular to line segment AB. Let
point P be the point of intersection.(Recall procedure for the construction of a
perpendicular line through a given point.(Figure3).
 using Q as the center point of compass, draw a circle through point P.
The three sides of triangle i.e. AB, BC, CA will be tangent to the circle and hence
circle inscribed in
ABC.
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