The radii of two concentric circles are 12 cm and 13 cm. AB is a diameter of the bigger circle. BD is a tangent to a smaller circle touching it at D. Find the length (in cm) of AD? (correct to one decimal place)
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 24.5
By the Pythagoras theorem in triangle ODB
⇒ OB2 = OD2 + BD2
⇒ 169 = 144 + BD2
⇒ BD2 = 25 cm
⇒ BD = 5 cm
⇒ BD = BE/2 (Perpendicular drawn from from the centre on the chord bisects in two equal parts)
⇒ BE = 10cm
In triangle ABE using Pythagoras theorem
⇒ 676 = 100 + AE2
⇒ AE2 = 576 cm
⇒ AE = 24 cm
In triangle ADE using Pythagoras theorem
⇒ AD2 = 576 + 25
⇒ √601 or 24.5 cm