In the given figure, MN is a tangent to a circle with centre 0. If ON= 15 cm and angle ONM=30°, then find the radius of the circle.
M
30°
N
O
15 cm
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Given : MN is a tangent to a circle with centre O.
ON= 15 cm and angle ONM=30°,
To find : the radius of the circle.
Solution:
MN is tangent to circle at point M
ON = 15 cm
OM = Radius = ?
∠OMN = 90° ( tangent)
∠ONM = 30° Given
Sin ∠ONM = OM/ON
=> Sin30° = Radius / 15
=> 1/2 = Radius /15
=> Radius = 15/2
=> Radius = 7.5 cm
radius of the circle. is 7.5 cm
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