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]

Also,

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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