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# A circle with center O has a chord CD inside it, such that points C an

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1370
Location: India
A circle with center O has a chord CD inside it, such that points C an  [#permalink]

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22 Jul 2018, 09:50
1
00:00

Difficulty:

35% (medium)

Question Stats:

80% (00:59) correct 20% (01:19) wrong based on 20 sessions

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A circle with center O has a chord CD inside it, such that points C and D lie on the circumference of the circle. CD is less than the diameter. A point E is taken on chord CD and O is joined with E. Is OE perpendicular to CD?

(1) OC = OD

(2) CE = ED
Director
Joined: 20 Feb 2015
Posts: 796
Concentration: Strategy, General Management
Re: A circle with center O has a chord CD inside it, such that points C an  [#permalink]

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22 Jul 2018, 11:33
1
amanvermagmat wrote:
A circle with center O has a chord CD inside it, such that points C and D lie on the circumference of the circle. CD is less than the diameter. A point E is taken on chord CD and O is joined with E. Is OE perpendicular to CD?

(1) OC = OD

(2) CE = CD

(1) OC = OD
will be the case for all the chords !!
insufficient.

(2) CE = CD
sufficient ,
C is on D so a definite no !!

unless it is CE=DE
in which case
sufficient , as any line from the center that bisects a chord is perpendicular to the chord

B
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1370
Location: India
Re: A circle with center O has a chord CD inside it, such that points C an  [#permalink]

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23 Jul 2018, 05:31
CounterSniper wrote:
amanvermagmat wrote:
A circle with center O has a chord CD inside it, such that points C and D lie on the circumference of the circle. CD is less than the diameter. A point E is taken on chord CD and O is joined with E. Is OE perpendicular to CD?

(1) OC = OD

(2) CE = CD

(1) OC = OD
will be the case for all the chords !!
insufficient.

(2) CE = CD
sufficient ,
C is on D so a definite no !!

unless it is CE=DE
in which case
sufficient , as any line from the center that bisects a chord is perpendicular to the chord

B

Hello

Sorry the question had a typo. The second statement should read CE = ED, which I have now corrected.
thanks
Re: A circle with center O has a chord CD inside it, such that points C an &nbs [#permalink] 23 Jul 2018, 05:31
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