Question

Two circles of radii 18 cm and 8 cm touch externally. Find the length of a direct common tangent to the two circles.

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Answer 1

Given that PA = 18 cm and QB = 8 cm

Then, AB = AC + CB = (18 + 8) cm = 26 cm.

PQ be a direct common tangent to the two circles.

We know that AP and BQ are $\perp$ PQ

Draw, BL$\perp$AP.

Then, PLBQ is a rectangle.

Now, LP = BQ = 8 cm and PQ = BL.

AL = (AP – LP) = (18 - 8) cm = 10 cm.

From $△$ALB, we have

${BL}^2$ = ${AB}^2$ – ${AL}^2$ = ${\left(26\right)}^2$ – ${\left(10\right)}^2$ = 676 - 100 = 576

$\Rightarrow$ BL = 24 cm.

PQ = BL = 24 cm.

Hence, the length of direct common tangent is 24 cm.