Mathematics
In the figure (i) given below, two circles with centers C, D intersect in points P, Q. If length of common chord is 6 cm and CP = 5 cm, DP = 4 cm, calculate the distance CD correct to two decimal places.
Circles
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Answer
From figure,
PM = MQ = = 3 cm.
In right △CMP,
⇒ CP2 = CM2 + PM2 (By pythagoras theorem)
⇒ 52 = CM2 + 32
⇒ CM2 = 25 - 9
⇒ CM2 = 16
⇒ CM = = 4 cm.
In right △DMP,
⇒ DP2 = DM2 + PM2 (By pythagoras theorem)
⇒ 42 = DM2 + 32
⇒ DM2 = 16 - 9
⇒ DM2 = 7
⇒ DM = = 2.65 cm.
CD = CM + MD = 4 + 2.65 = 6.65 cm.
Hence, CD = 6.65 cm.
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