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the length of a chord of circle is 4cm. If it's perpendicular distance from the centre is 1.5 cm, determine the radius of the circle​

the length of a chord of circle is 4cm. If it's perpendicular distance from the centre is 1.5 cm, determine the radius of the circle​

Grade:12

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
3 years ago
Let O be the Center.

Let BC be the chord of 4 cm

A is a point on chord BC so that OA is 1.5 cm

OA is also perpendicular to chord BC

Since, Perpendicular from the Center to the chord , bisect the chord ( a property of circle)

BA = 2 cm

Now, In triangle OAB by Pythagoras theorem

OB^2 = OA^2 + BA^2

OB^2 = 2^2 + 1.5^2

= 4 + 2.25

OB^2 = 6.25

OB = 2.5 com

So radius of the circle = 2.5 cm

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