The distance between centers of the two circles is 10 cm and the two circles radii are 3 and 5 cm respectively. What is the length of the transverse common tangent?

8 cm

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2 cm

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4 cm

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6 cm

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Solution

The correct option is D 6 cm
Given: $D = 10$ cm
Circles radii $=$ $r_{1} + r_{2} = 3 + 5 = 8$ cm
Length of the transverse common tangent $=$ $\sqrt{d^{2} - (r_{1} + r_{2})^{2}}$
$=$ $\sqrt{10^{2} - 8^{2}}$
$=$ $\sqrt{100 - 64}$
$=$ $\sqrt{36}$
$= 6$ cm

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The distance between centers of the two circles is 10 cm and the two circles radii are 3 and 5 cm respectively. What is the length of the transverse common tangent?

The correct option is D 6 cmGiven: D=10 cmCircles radii = r1+r2=3+5=8 cmLength of the transverse common tangent = √d2−(r1+r2)2= √102−82= √100−64= √36=6 cm

The correct option is D 6 cm
Given: $D = 10$ cm
Circles radii $=$ $r_{1} + r_{2} = 3 + 5 = 8$ cm
Length of the transverse common tangent $=$ $\sqrt{d^{2} - (r_{1} + r_{2})^{2}}$
$=$ $\sqrt{10^{2} - 8^{2}}$
$=$ $\sqrt{100 - 64}$
$=$ $\sqrt{36}$
$= 6$ cm