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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses