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In the figure below, AB is the chord of a circle with center [#permalink]

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21 Oct 2010, 02:02

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In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ACD= y degrees and AOD = x degrees such that x = ky, then the value of k is

In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ACD= y degrees and AOD = x degrees such that x = ky, then the value of k is

A. 3 B. 2 C. 1 D. None of the above

ans : OB=BC thus, in the triangle BOC, angle BOC = angle BCO =y again, OB=AO (as both are radii of the same circle) thus, in triangle OAB, angleOAB= angle OBA =y (because OAB and BOC are equal triangle) thus, we can make the equation like this, 180=y+(180-2y)+x thus, y=x thus, ans is c

In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ACD= y degrees and AOD = x degrees such that x = ky, then the value of k is

A. 3 B. 2 C. 1 D. None of the above

please help me with answers in details.

OB=BC, So BCO=BOC=x ABO=2x (exterior angle of triangle BOC, sum of the two opposite interior angles) OAB=ABO=2x (Isosceles triangle, 2 sides are the radius of the circle) AOD is an exterior angle of triangle AOC Hence AOD=OAB+BCO=x+2x=3x=y

In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ACD= y degrees and AOD = x degrees such that x = ky, then the value of k is

A. 3 B. 2 C. 1 D. None of the above

please help me with answers in details.

Sol: OB = BC (given) => Angle BOC = Angle BCO = y => Angle OBC = 180-2y (in triangle OBC) Hence Angle OBA = 2y Since AO = OB (Both radius of the circle) so Angle OBA = Angle BAO = 2y => Angle AOB = 180 -4y Now we know all the three angles at point O form by a straight line DC Hence Angle AOD + Angle AOB + Angle BOC = 180 x + 180 - 4y + y = 180 x - 3y = 0 x = 3y Answer (A)

gmatclubot

Re: Geomtery, circles
[#permalink]
21 Oct 2010, 22:08

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