O is the midpoint of line segment AB of length 36 cm. If the semicircles are drawn on AB, OA and OB as diameters, then the radius of the smallest circle whch touches all the semicircles is

6 cm

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9 cm

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12 cm

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4 cm

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Solution

The correct option is A 6 cm

In $Δ P O Q,$
By pythagoras theorem,
$(Q P)^{2} = (O P)^{2} + (O Q)^{2}$
$(r + 9)^{2} = (18 - r)^{2} + 9^{2}$
$r^{2} + 81 + 18 r = 324 + r^{2} - 36 r + 81$
$54 r = 324$
$r = 6$
Hence, option a is correct.

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O is the midpoint of line segment AB of length 36 cm. If the semicircles are drawn on AB, OA and OB as diameters, then the radius of the smallest circle whch touches all the semicircles is

The correct option is A 6 cm In ΔPOQ, By pythagoras theorem, (QP)2=(OP)2+(OQ)2 (r+9)2=(18−r)2+92 r2+81+18r=324+r2−36r+81 54r=324 r=6 Hence, option a is correct.

The correct option is A 6 cm

In $Δ P O Q,$
By pythagoras theorem,
$(Q P)^{2} = (O P)^{2} + (O Q)^{2}$
$(r + 9)^{2} = (18 - r)^{2} + 9^{2}$
$r^{2} + 81 + 18 r = 324 + r^{2} - 36 r + 81$
$54 r = 324$
$r = 6$
Hence, option a is correct.