Two parallel chords are drawn in a circle of
diameter 300 cm. The length of one chord is
24.0 cm and the distance between the two
chords is 21.0 cm; find the length of the other
chord.

Asked by siddeshmankar90.9spicertl | 6th Feb, 2021, 02:16: PM

Expert Answer:

Let AB = 24 cm be the first chord and CD be the second chord in the circle with centre O.
P and Q are on AB and CD bisecting them respectively.
So, AP = PB = 12 cm
In triangle APO, by Pythagoras theorem we have
PO2 = AO2 - AP2 = 152 - 122 = 81
Therefore, PO = 9 cm
So, we get OQ = 21 - 9 = 12 cm
In triangle COQ, by Pythagoras theorem we have
CQ2 = CO2 - OQ2 = 152 - 122 = 81
Therefore, CQ = 9 cm
Thus, CD = 2CQ = 18 cm

Answered by Renu Varma | 9th Feb, 2021, 12:55: PM