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655-705 (Hard)|   Geometry|      
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Bunuel
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If BD=DC, what is the value of x in the figure above? 14 May 2021, 01:30
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E
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Difficulty:

55% (hard)

Question Stats:

57% (01:47) correct 43% (02:43) wrong based on 104 sessions

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If BD=DC, what is the value of x in the figure above?

A. 75
B. 95
C. 97.5
D. 100
E. 105



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E
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If BD=DC, what is the value of x in the figure above? 14 May 2021, 03:40
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Creating a joining line between B and C, you create a triangle DCB. As angle D within the circle is 30' the other two angles will be 75'.

Joining B and C also creates a quadrilateral ABCD. As angle C is 75', and opposite angles of a quadrilateral sum to 180: x+75=180
x=105

Answer E
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If BD=DC, what is the value of x in the figure above? 14 May 2021, 11:57
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Join B to C.

We get a triangle BCD where angle DBC = angle DCB = 75
Now ABCD is a cyclic quadrilateral and we know that sum of opposite angles of a cyclic quadrilateral = 180
angle BCD + angle BAD = 180
75 + angle BAD = 180
angle BAD = 105

IMO E
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If BD=DC, what is the value of x in the figure above? 14 May 2021, 21:00
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If BD=DC and we join B and C together then, angle B = angle C= \(\frac{(180-30)}{2}\) =75

In a circle, sum of opposite angles of a rectangle = 180 degree
So, x + 75 = 180 or, x = 105 degree

So, I think E. :)
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If BD=DC, what is the value of x in the figure above? 31 Aug 2021, 19:13
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You can answer the question by using the Arc Degree measures.

Rule: inscribed angle = (1/2) * (the central angle created by the same arc that creates the inscribed angle


<BAD = X = inscribed angle of Arc BCD


(1st) can find Arc BC by doubling the inscribed angle 30 deg.

Arc BC = 60 deg.

(2nd) joint point B to C to create the isosceles triangle

Angle <CBD = 75 deg. ———-> this is the inscribed angle created by Arc CD

Arc CD = (2) (75) = 150 deg.


(3rd) the Central Angle sub tended by Arc BCD = (60) + (150) = 210

The inscribed angle <BAD subtended by the Same Arc BCD will be (1/2) the value of 210 deg. or


X = 105 deg

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If BD=DC, what is the value of x in the figure above? 01 Sep 2021, 09:40
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Angle x = (Angle subtended at center by arc BCD)/2

= (75*2+30*2)/2

= 105
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If BD=DC, what is the value of x in the figure above? 03 Aug 2023, 01:32
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