Question

OR
3
The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a
tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find
the length of AP.
1
1
1
A
TCT​

Answer 1

Produce BD to meet the bigger circles at E. Join AE.

Then ∠AEB = 90° [Angle in a semicircle]

OD ⊥ BE ['.' BE is tangent to the smaller circle at D and OD is its radius]

BD = DE ['.. BE is a chord of the circle and OD ⊥ BE] . ..

OD || AE [. .. ∠AEB = ∠ODB = 90°]

In ΔAEB O and D are mid-points of AB and BE. Therefore, by mid-Point theorem,

we have =

AD = 19 cm