find the distance between two parallel chords of lengths 24cm and 32cm ,if they lie on same side of centre and radius of the circle is 20 cm .
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AB = 24 cm , BP = 24/2 = 12 cm
CD = 32 cm ,MD = 32/2 = 16 cm
OD = OB = 20 cm ( given radius )
in triangle OMD
(OM) ^2 = ( OD) ^2 - (MD)^2
OM ^ 2 = 20*20 - 16*16 = 400-256= 144
OM = √144 = 12 cm
in triangle OPM
(OP) ^2 = (OB) ^2 - (BP)^2
(OP ) ^ 2 = 20*20-12*12 = 400-144 = 256
OP = √256
OP = 16 cm
PM = OP -OM
PM = 16-12=4 cm
CD = 32 cm ,MD = 32/2 = 16 cm
OD = OB = 20 cm ( given radius )
in triangle OMD
(OM) ^2 = ( OD) ^2 - (MD)^2
OM ^ 2 = 20*20 - 16*16 = 400-256= 144
OM = √144 = 12 cm
in triangle OPM
(OP) ^2 = (OB) ^2 - (BP)^2
(OP ) ^ 2 = 20*20-12*12 = 400-144 = 256
OP = √256
OP = 16 cm
PM = OP -OM
PM = 16-12=4 cm
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