Two parallel chords AB and CD are 3.9cm apart and lie on the opposite sides of the centre of a circle. If AB = 1.4cm and CD = 4cm, find the radius.

Asked by pereiracalida | 9th Jan, 2018, 06:54: PM

Expert Answer:

begin mathsize 16px style We space have
AB equals 1.4 space cm comma space CD equals 4 space cm space and space PQ equals 3.9 space cm
rightwards double arrow AP equals PB equals 1 half AB equals 0.7 space cm space space and space space CQ equals QD equals 1 half CD equals 2 space cm
If space OQ equals straight x comma space then space OP equals left parenthesis 3.9 minus straight x right parenthesis space cm
Let space OC equals OA equals straight r space left parenthesis radius space of space the space circle right parenthesis
In space right minus angled space triangle OPA comma
OA squared equals OP squared plus AP squared
rightwards double arrow straight r squared equals left parenthesis 3.9 minus straight x right parenthesis squared plus left parenthesis 0.7 right parenthesis squared space space space space space space space space.... left parenthesis straight i right parenthesis
In space right minus angled space triangle OQC comma
OC squared equals OQ squared plus CQ squared
rightwards double arrow straight r squared equals left parenthesis straight x right parenthesis squared plus left parenthesis 2 right parenthesis squared space space space space space space space space.... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma
left parenthesis 3.9 minus straight x right parenthesis squared plus left parenthesis 0.7 right parenthesis squared space space equals left parenthesis straight x right parenthesis squared plus left parenthesis 2 right parenthesis squared
rightwards double arrow 15.21 minus 7.8 straight x plus straight x squared plus 0.49 equals straight x squared plus 4
rightwards double arrow 15.7 minus 7.8 straight x equals 4
rightwards double arrow 7.8 straight x equals 11.7
rightwards double arrow straight x equals 1.5 space cm
Thus comma space the space radius space of space the space circle space is space 1.5 space cm. end style

Answered by Rashmi Khot | 10th Jan, 2018, 09:41: AM