A circle has radius cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in major segment is 45º.
A circle with radius cm is divided into two segments by a chord of length 2 cm.
We have drawn a circle having centre O
Let AB = 2 cm be the required chord which divides the circle into two segment.
To Prove: the angle subtended by the chord at a point in major segment is 45º.
Which means we have to prove that APB = 45°
We have, radius = cm
OA = OB = cm (given)
OA2 = OB2 = 2 cm
Also, chord AB = 2 cm (given)
AB2 = 4cm
Now, we can see that in DAOB,
OA2 + OB2 = AB2
As, 2 + 2 = 4
So this follows Pythagoras theorem.
Hence AOB = 90°
Now we know that angle subtended at the centre by an arc is twice the angle subtended by it at any part of the circle
Hence proved.