Q. 184.0( 8 Votes )

The radii of two

Answer :

Given: The radii of two concentric circles with the same center as O are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is tangent to the smaller circle touching it at D and intersecting the larger circle at P, on producing

To Find: length of AP

Construction: Join OD

Clearly OB AC  [As a tangent to at any point on the circle is perpendicular to the radius through the point of contact]


PD = BD  [Perpendicular through the center to a chord in a circle bisects the chord]
i.e. D is the mid-point of BP.

Also, O is the mid-point of AB.

So, We can use the mid-point theorem and we will have
[Mid-point theorem: The segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.]
AP = 2OD
OD is radius of smaller circle, therefore
AP = 2(8) = 16 cm

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