The radii of two concentric circles are 12 cm and 13 cm AB is a diameter of the bigger circle BD is ...........

Quantitative Aptitude (CGL) Geometry

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 touchingit at D. Find the length (in cm) of AD? (correct to one decimal place)

This questions was previously asked in

SSC CGL 13th August 2021 Shift-3

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24.5

23.5

25.5

17.6

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Explanation:

Correct option 1) 24.5

Solution

Radus of bigger circle= 13 cm

Radius of smaller circle=12 cm

AB is the diameter of bigger circle and AD is the diameter of smaller circle.

By Pythagoras Theorem; in triangle ODB
OB² = OD² + BD²
169 =144+ BD²
⇒ BD = 5 cm
BD = DE = 1/2 × BE
[Perpendicular drawn from the center on a chord bisects it in two equal parts]
⇒ DE = BD = 5 cm
⇒ BE = 10 cm
In triangle ABE,
[Angle made in semicircle]
AB² = EB²+ AE²
⇒676 = 100+ AE²
= AE = √576
= AE = 24 cm
In triangle ADE
⇒ AD² = ED² + AE²
⇒ AD2 = 25+ 576
⇒ AD² = 601
⇒ AD = √601
⇒ AD = 24.51 cm
So, the length of AD = 24.5 (Approximately)