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Let be a diameter of a circle of length
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
Let
A
C
AC
A
C
be a diameter of a circle of length
20
cm
20\,\text{cm}
20
cm
. Point
B
B
B
lies on the circle and the perpendicular from
B
B
B
to
A
C
AC
A
C
meets
A
C
AC
A
C
at
D
D
D
. (a) Show that
∠
A
B
C
=
90
∘
\angle ABC = 90^{\circ}
∠
A
B
C
=
9
0
∘
. (b) Prove that
B
D
2
=
A
D
⋅
D
C
BD^{2} = AD \cdot DC
B
D
2
=
A
D
⋅
D
C
. (c) If
A
D
=
8
cm
AD = 8\,\text{cm}
A
D
=
8
cm
, calculate
B
D
BD
B
D
.
Related theory
Circles
Similarity of Triangles
Similarity
Pythagoras theorem
Triangles
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