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In an isosceles triangle with
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
In an isosceles triangle
A
B
C
ABC
A
B
C
with
A
B
=
A
C
=
7
cm
AB = AC = 7\,\text{cm}
A
B
=
A
C
=
7
cm
, the point
D
D
D
lies on
B
C
BC
B
C
such that
∠
B
A
D
=
∠
C
A
D
\angle BAD = \angle CAD
∠
B
A
D
=
∠
C
A
D
. (i) Prove that the points
A
,
B
,
C
A,\,B,\,C
A
,
B
,
C
and
D
D
D
are concyclic. (ii) Show that
B
D
=
D
C
BD = DC
B
D
=
D
C
. (iii) If
B
C
=
8
cm
BC = 8\,\text{cm}
B
C
=
8
cm
, find the lengths of
B
D
BD
B
D
and
D
C
DC
D
C
. State the reasons used at each step.
Related theory
Quadrilaterals
Triangle Congruence
Triangle Congruence Criteria
Triangles
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