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The centres of two circles with radii 28 cm and 20 cm are 50 cm apart. What is the length (in cm) of the transverse common tangent?
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14
Use the Pythagorean triplet logic: (R+r)=48 and d=50. The triangle formed has sides 48, 50, and x. Since 502тИТ482=2500тИТ2304=196=142, the answer is 14.
Radius of first circle R = 28 cm, Radius of second circle r = 20 cm, Distance between centers d = 50 cm.
L=d2тИТ(R+r)2тАЛ
Use the Pythagorean triplet logic: (R+r)=48 and d=50. The triangle formed has sides 48, 50, and x. Since 502тИТ482=2500тИТ2304=196=142, the answer is 14.
Confusing the formula for transverse common tangent with the direct common tangent. The direct common tangent formula uses (RтИТr)2, while the transverse uses (R+r)2.
Identify parameters
Identify the radii R=28, r=20 and the distance between centers d=50.
R=28,r=20,d=50
Apply Transverse Tangent Formula
The length of the transverse common tangent L is given by d2тИТ(R+r)2тАЛ.
L=502тИТ(28+20)2тАЛ
Calculation
Perform the arithmetic: 502=2500 and 482=2304. Then subtract and find the square root.
L=2500тИТ2304тАЛ=196тАЛ=14
D is correct because the calculated transverse common tangent length is 14 cm.
This is a direct application of the Pythagorean theorem in coordinate geometry; remember that (R+r) forms one side of the right triangle for transverse tangents, whereas (RтИТr) is used for direct tangents.
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