A circle is inscribed in an equilateral triangle. Radii to two of the

Question

https://gmatclub.com/forum/download/file.php?id=58612 A circle is inscribed in an equilateral triangle. Radii to two of the points of tangency are shown. What is x? A. 120° B. 150° C. 180° D. 210° E. 240° Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 2020-10-27_14-09-35.png

mdsaddamforgmat · Answer

IMO: E

angle between Radius & Tangent is 90deg
one angle of triangle is 60deg (Equilateral triangle)
We know, sum of all angle of Quadrilateral = 360deg
Therefore, 60 + 2x90 +(360-X) = 360 deg
or, X=240Deg

Wizbiz · Answer

OPTION E
ANGLE BY THE EQUILATERAL TRIANGLE=60 degrees at each of the vertices.
Thus, angle CDB in quadrilateral ABCD = 180-60=120 (opposite angles in a quadrilateral)
An arc  subtends double an angle at the center than at any other point in the circle. 
Thus, angle BOC = 2*120=240 degrees.

Suvek · Answer

1. Radius of Circle touches the equilateral triangle sides at point of tangency. This implies radius is perpendicular to sides of equilateral triangle
2. Given triangle is equilateral implies each angle of triangle is 60 degrees.
3. Total angle sum of a quadilateral is 360 degrees. Here angles of quadilateral include two angles at point of tangency, one angle of triangle and last the angle formed by the radii of circle( Let it be y ). Hence 90+90+60+y =360. Hence y is 120 degrees.
4. Angle formed at a point is 360 degrees. Hence the angle x = 360 - 120 = 240 degrees.

Solution is E

Pankaj0901 · Answer

ANSWER E

Sum of angles of a quadrilateral= 360 deg
Angle between tangent and radius= 90 deg.
Angle of an equilateral triangle= 60 deg
so, angle opposite to x = 360-90-90-60=120
x= 360-120 =240

carouselambra · Answer

Missing angle in the quadrilateral can be found by : 360- (90+90+60)
Using the measure of tangents and angle of an equ. triangle.
Hence, 120 degrees is the measure.

To find x, we know that 360-120 will give us the answer using the reflex angle measurement property.
 240 will be the measure of x.

am0804 · Answer

IMO E.

We can find out 'x' by finding the other part of the central angle formed at the center of the circle.  The 2 radii + sides of the triangle form a quadrilateral, so the sum of all angles should be 360.

- Since the triangle is equilateral, each angle will be 60 degrees. Thus, the top vertex angle is 60. 
- Angle is 90 degree at point of tangency. So other 2 angles are 90 degrees each.

360 - (60+90+90) = 120. 
120 + x = 360 
=> x = 240

A circle is inscribed in an equilateral triangle. Radii to two of the

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A circle is inscribed in an equilateral triangle. Radii to two of the

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