Length of a tangent segment drawn from a point outside a
circle is 8 cm and distance of the point from the centre of circle is 10 cm. Find the diameter of the circle.
circle is 8 cm and distance of the point from the centre of circle is 10 cm. Find the diameter of the circle.
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Answer:
The length of the tangent is 15cm.
Explanation:
Let O be the center of the given circle.
Let P be a point, such that
OP 17 cm.
Let OT be the radius, where
OT = 5cm
Join TP where TP is a tangent.
Now, tangent drawn from an external
point is perpendicular to the radius at
the point of contact.
OT LPT
In the right A OTPwe have:
Op? = OT2 + TP2
By
Pythagoras' theorem:]
TP = = VOP2, - OT2
= V172-8
= 289 64
= 225
= 15 cm
The length of the tangent is 15 cm.
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