#SSC CGL

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Question : Observe the given figure. The distance between the two centres AB is:

Option 1: 10 cm
Option 2: 11 cm
Option 3: 13 cm
Option 4: 12 cm

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Answer (1)

Team Careers360 24th Jan, 2024

Correct Answer: 13 cm

Solution :
Construction: Draw a perpendicular from $A$ to $E$.
Since OC and OD are tangents, $\angle ACD$ = $\angle BDC = 90^\circ$
$AEDC$ forms a rectangle.
Applying Pythagoras theorem in $\triangle AEB$,
$AB^2 = AE^2+EB^2$
⇒ $AB^2 = CD^2+(BD-DE)^2$
⇒ $AB = \sqrt{(8-3)^2+12^2}$
⇒ $AB=\sqrt{25+144}$
⇒ $AB = 13$ cm
Hence, the correct answer is 13 cm.

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