8. In fig. 28.20, AB is a diameter
and Y is a point on the circle. y
IFAY=5 cm and BY = 12 cm,
find the radius of the circle.
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Answer:
In the given figure,
The length of tangent AB = distance between centres C1 and C2 of the two circles = 26 cm.
Radius of circle 1 =5cm
Radius of circle 2 =5cm
Using the property that Common tangents of two cirles intersect the line joining centres in the ratio of their radii, we can see that O is the mid point of both the centres C1 and C2.
⇒OC1=OC2=13cm.
In Right Triangle OCC1, using pythagoras theorem,
OC=
(13
2
−5
2
)
= 12 cm.
SImilarly, OD=12 cm
Lenghtoftangent=OC+OD=24cm.
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