Mathematics
In the given figure, O and O' are centers of two circles, AB // CD // OO', then which of the following is not true :
AB = 2 × OO'
CD = 2 × OO'
AB = CD
AB ≠ CD
Circles
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Answer
Draw ON and O'M perpendicular to AB.
We know that,
Perpendicular from center to the chord bisects it.
∴ AN = NP and MP = MB
From figure,
⇒ AB = AN + PN + MP + MB
⇒ AB = PN + PN + MP + MP
⇒ AB = 2PN + 2MP
⇒ AB = 2(PN + MP)
⇒ AB = 2NM
⇒ AB = 2OO' …………(1)
Draw OE and O'F perpendicular to CD.
We know that,
Perpendicular from center to the chord bisects it.
∴ CE = EQ and QF = FD
From figure,
⇒ CD = CE + EQ + QF + FD
⇒ CD = EQ + EQ + QF + QF
⇒ CD = 2EQ + 2QF
⇒ CD = 2(EQ + QF)
⇒ CD = 2EF
⇒ CD = 2OO' …………(2)
From equation (1) and (2), we get :
⇒ AB = CD.
Hence, Option 4 is the correct option.
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