SSC CPO 2022 PYQ — Question 142

The correct answer is option 2 i.e. 23.58 Units

Given:-
AB is a common tangent to C(c, 5cm) and C(d, x cm)
Thus, ang(CAE) = ang(DBE) = 90 degree

AC = 5 units
AE = 8 units
BE = 12 units

To find:-
Length of the line joining the centers of both circles (CD)

Solution:-
We know CD = CE + DE

We know in △AEC
AE² + AC² = CE² (By Pythagorus Theorem)
25 + 64 = CE²
CE² = 89
CE ~ 9.43 units

In △BDE

we have to find 'x'.

Thus we will use similarity rules to find the value of 'x'.

Thus, In △AEC and △BDE

ang(CAE) = ang(DBE) (both are 90º, as AB is tangent to both the circles)

ang(AC) = ang(DEB) (Vertically Opposite Angles are equal)

Thus, due to A.A similarity rule

△AEC ~ △BED

Thus, x = 7.5 cm

Now in △BDE

ED² = BE² + BD²

ED² = 12² + 7.5²

ED² = 200.25

ED ~ 14.15

Thus, CD = CE + ED

CD = 9.43 + 14.15 

CD = 23.58