Construct a direct common tangent to two circles of radii 4 cm and 2 cm whose centers are 8 cm apart. Measure and verify the length of the tangent.

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7.75 cm

5.75 cm

7.70 cm

2.75 cm

answer is A.

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Detailed Solution

Given,
Circle C1 with radius

r_{1}

= 4 cm center A
Circle C2 with radius

r_{2}

= 2 cm center B
Distance between center d= 8 cm
So length of tangent,

PQ = \sqrt{d^{2} - {(r_{1} - r_{2})}^{2}}

PQ = \sqrt{8^{2} - {(4 - 2)}^{2}}

PQ = \sqrt{8^{2} - 2^{2}}

PQ = 7.75 cm

Now, make a line AB with measure of 8 cm.
From point A make a circle C1 of radius 4 cm with center A.
From point B make a circle C2 of radius 2 cm with center B.
From point A make another circle C3 of radius (4-2)=2 cm with center A.
Now from the midpoint of AB, M draw another circle C4 with radius 4 cm.
At point where circle C4 cuts C3, E and F join them with A to make AE and AF
Here extent AE and AF to P and R respectively to meet C1.
Make,
BQ∥AP and BS∥AR
Join P to Q and R to S
So, we get
Direct tangents = PQ and RS.
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