What is the value of x?
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Hi AAPL,If a circle is circumscribed around a quadrilateral, as shown above, what is the value of x?
A. 105
B. 110
C. 115
D. 120
E. 125
The OA is C.
I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.
Let's take a look at your question.
We know that the in a circle when two chords of a circle make an angle at the circumference of the circle, the arc subtended by that angle is always twice the angle.
Therefore, in the circle given,
$$2x\ =\ arclength\ \left(BAD\right) ... (i)$$
$$2\times65\ =\ arclength\ \left(BCD\right)$$
$$\ 130=\ arclength\ \left(BCD\right ... (ii))$$
Adding Eq(i) and (ii),
$$\ 2x+130=\ arclength\ \left(BAD\right)+\ arclength\ \left(BCD\right)$$
$$\ 2x+130=\ 360$$
$$\ 2x=\ 360-130$$
$$\ 2x=\ 230$$
$$\ x=\ \frac{230}{2}=115$$
Therefore, Option C is correct.
Hope it helps.
I am available if you'd like any follow up.
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Hi AAPL,
This question is built around one specific Geometry rule: when a quadrilateral is inscribed in a circle, opposite angles sum to 180 degrees. Thus, angle X =180 - 65 = 115 degrees.
Final Answer: C
GMAT assassins aren't born, they're made,
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This question is built around one specific Geometry rule: when a quadrilateral is inscribed in a circle, opposite angles sum to 180 degrees. Thus, angle X =180 - 65 = 115 degrees.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich