Question

The distance between the centers of two circles of radius 7.5 cm and 2.5 cm is 19 cm. What is the length (in cm) of transverse common tangent?

Answer 1

Given :- The distance between the centers of two circles of radius 7.5 cm and 2.5 cm is 19 cm.

To Find :- The length (in cm) of transverse common tangent ?

Solution :-

We know that,

• Transverse common tangent = √[D² - (r1 + r2)²]
• D = Distance between centre of both circles .
• r1 = Radius of first circle .
• r2 = Radius of second circle .

So, from given data we have,

• D = 19 cm
• r1 = 7.5 cm
• r2 = 2.5 cm

then,

→ Length of transverse common tangent = √[D² - (r1 + r2)²]

→ Length of transverse common tangent = √[19² - (7.5 + 2.5)²]

→ Length of transverse common tangent = √[361 - 10²]

→ Length of transverse common tangent = √(361 - 100)

→ Length of transverse common tangent = √(261)

→ Length of transverse common tangent = √(3 * 3 * 29)

→ Length of transverse common tangent = 3√29 cm (Ans.)

Hence, the length of transverse common tangent is equal to 3√29 cm .

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