In the given figure, the radii of two concentric circles are 12 cm and 7 cm. AB is the diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D. Find the length AD.
Answer:
17.06 cm
- We know that angle in a semicircle is of 90∘. So, ∠AEB=90∘.
- We also know that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
So, OD⊥BE and OD bisects BE. - Using Pythagoras' theorem in right △OBD, we have OB2=OD2+BD2 It is given that OB=12 cm and OD=7 cm. ⟹BD=√OB2−OD2=√(12)2−(7)2 cm=√95 cm Now, BE=2BD=2√95 cm. [ D is the midpoint of BE ]
- Using Pythagoras' theorem in right △AEB, we have As, is the diameter of the circle, =
- Using Pythagoras' theorem in right , we have
We know that