Question

1. In the figure '0' is the centre of the circle. AB= 10 cm, CD = 1 cm. If C is the midpoint of the chord AB, find the radius of the circle if AB perpendicular to CD.
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Answer 1

The length of the radius of the given circle is 13 cm.

Given:

AB = 10 cm

CD = 1 cm

C is the midpoint of AB

AB is perpendicular to CD

To Find:

We need to find the length of the radius of the circle

Solution:

We know that perpendicular from the center bisects the chord and since C is the midpoint of AB, OC will be perpendicular to AB.

AC = BC = 5cm

Let the radius of the circle be R

Then, BO = R and OC = R - 1

In triangle BOC, using Pythagoras theorem, we get-

BO² = OC² + BC²

R² = (R-1)² + 5²

R² = R² + 1 -2R + 25

2R = 26

R = 13

Thus, the length of the radius of the given circle is 13 cm.

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