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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 | 06 Feb, 2021, 02:16: PM
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 | 09 Feb, 2021, 12:55: PM

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