Question : AB is the common tangent to both circles as shown in the given figure. What is the distance between the centres of the circles?
Option 1: 20 cm
Option 2: 15 cm
Option 3: 10 cm
Option 4: 30 cm
Correct Answer: 30 cm
Solution : Given that AB is the common tangent to both circles. In the circle with centre C, $\angle$CAE = 90° In the circle with centre D, $\angle$DBA = 90° and $\angle$AEC = $\angle$BED (vertically opposite angle) So, $\triangle$CAE $\sim$ $\triangle$DBC ⇒ $\frac{CA}{AE}=\frac{DB}{BE}$ ⇒ $\frac{4}{3}=\frac{DB}{15}$ ⇒ DB = $\frac{4×15}{3}$ = 20 cm In $\triangle$CAE, ⇒ CE2 = AC2 + AE2 ⇒ CE2 = 42 + 32 = 52 ⇒ CE = 5 cm In $\triangle$DBE, ⇒ DE2 = DB2 + BE2 ⇒ DE2 = 202 + 152 = 252 ⇒ DE = 25 cm $\therefore$ The distance between the centres of the circle = CE + DE = 5 + 25 = 30 cm Hence, the correct answer is 30 cm.
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Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Question : Directions: Select the option in which the given figure (X) is embedded (rotation is NOT allowed).
Question : AB is a common tangent to both the circles in the given figure. Find the distance (correct to two decimal places) between the centres of the two circles.
Option 1: 18.98 units
Option 2: 23.58 units
Option 3: 26.59 units
Option 4: 21.62 units
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