Find the radiuns of a circle if the length of a tangent from an external point 10 cm away from the centre is 6 cm.
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Draw a circle of radius 6cm with center O. Draw a line segment of 10cm away from point/center O
Mark midpoint of OP and draw a circle of radius OQ=5cm
This circle cuts the initial circle at two points M and N. Join MP and NP are the required tangents.
We know, PM=PN (tangent to a circle from external point)
In △ONP,(ON) 2 +(PN) 2
=(OP) 2
(PN) 2 =(OP) 2 −(ON) 2 =(10) 2 −6 2 =64
PN=8cm
Step-by-step explanation:
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