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Triangle is inscribed in a circle with centre such that
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
Triangle
A
B
C
ABC
A
B
C
is inscribed in a circle with centre
O
O
O
such that
A
B
=
A
C
AB = AC
A
B
=
A
C
. The radii
O
B
OB
O
B
and
O
C
OC
O
C
are drawn. (i) Prove that
∠
B
O
A
=
∠
A
O
C
\angle BOA = \angle AOC
∠
B
O
A
=
∠
A
O
C
. (ii) Hence show that
∠
B
O
C
=
2
∠
B
A
C
\angle BOC = 2\angle BAC
∠
B
O
C
=
2∠
B
A
C
. (iii) If
∠
B
O
C
=
100
∘
\angle BOC = 100^\circ
∠
B
O
C
=
10
0
∘
, calculate the measures of
∠
B
A
C
\angle BAC
∠
B
A
C
,
∠
A
B
C
\angle ABC
∠
A
B
C
and
∠
A
C
B
\angle ACB
∠
A
C
B
.
Related theory
Properties of Triangles
Triangle Properties
Circles
Circle angle properties
Angle subtended by a chord
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