For a chord bisecting a diameter
of a circle at right angles as shown below,
To prove it complete the triangle
with one side as diameter to give the diagram below.
The triangles
and
are
similar, since both are right angled and angle
andare
similar, since both are right angled and angle
If angle
then
from triangle ABD,
and
from angle
then
from triangle ABD,and
from angle
Equating these gives
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