A point P is 13 cm from the centre of the circle. The length of tangent drawn from P to the circle is 12 cm. Find the radius of the circle.
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Given : P is a point at distance of 13cm from the centre of a circle O. The length of tangent drawn from P to the circle is 12 cm.
It is required to measure the radius of the circle.
Now, ∠OTP= 90°
( ∵ a tangent to a circle is ⊥ to the radius through the point of contact).
∴ In right angle triangle OTP,
OP² = OT²+ TP²
Or, 13² = OT² + (12)²
Or, 169-144 = OT²
Or, 25 = OT²
∴ OT = 5 cm
Hence, Radius = 5 cm
Answered by
3
GIVEN
P IS 13CM FRM THE CENTRE
LENGTH OF TANGENT IS 12
P=13
Q=12
TO FIND
RADIUS OF CIRCLE=?
R=?
THN ,
WE KNOW THAT THE TANGENT OF CIRCLE IS PERP TO THE R OF CIRCLE
ACCORDING TO THE PYTHAGORAS THEROM
P²=Q²+R²
R²=P²-Q²
R²=169-144
R=√25
R=5
HENCE,
RADIUS IS 5
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