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655-705 (Hard)|   Geometry|      
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Kritisood
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A circle is inscribed inside a right triangle as shown. If angle CAB = Updated on: 19 Jul 2020, 09:03
Originally posted by Kritisood on 19 Jul 2020, 08:56.
Last edited by Kritisood on 19 Jul 2020, 09:03, edited 1 time in total.
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55% (hard)

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61% (02:10) correct 39% (02:08) wrong based on 130 sessions

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Attachment:
Screenshot 2020-07-19 at 9.25.53 PM.png
Screenshot 2020-07-19 at 9.25.53 PM.png [ 20.11 KiB | Viewed 3514 times ]
A circle is inscribed inside a right triangle as shown. If angle CAB = 60º, what is angle COE? (Note: Figure not drawn to scale.)

A. 120º
B. 135º
C. 150º
D. 165º
E. 180º
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D
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A circle is inscribed inside a right triangle as shown. If angle CAB = 19 Jul 2020, 09:00
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Kritisood
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Screenshot 2020-07-19 at 9.25.53 PM.png
A circle is inscribed inside a right triangle as shown. If angle CAB = 60º, what is angle EOD? (Note: Figure not drawn to scale.)

A. 120º
B. 135º
C. 150º
D. 165º
E. 180º
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Answer would be Option A.please check the options again

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A circle is inscribed inside a right triangle as shown. If angle CAB = 19 Jul 2020, 09:04
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chipsy
Kritisood
Attachment:
Screenshot 2020-07-19 at 9.25.53 PM.png
A circle is inscribed inside a right triangle as shown. If angle CAB = 60º, what is angle EOD? (Note: Figure not drawn to scale.)

A. 120º
B. 135º
C. 150º
D. 165º
E. 180º


Answer would be Option A.please check the options again

Posted from my mobile device
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apologies, corrected the question.
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A circle is inscribed inside a right triangle as shown. If angle CAB = 19 Jul 2020, 13:01
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the radius from the center of the circle to the point of tangency is perpendicular to the tangent line

angle EOD = 360-90-90-60=120

Also, tangent segments to a circle from the same external point are congruent

DC=CF=r

angle COD =45

angle COE= 120+45 = 165


Kritisood
Attachment:
Screenshot 2020-07-19 at 9.25.53 PM.png
A circle is inscribed inside a right triangle as shown. If angle CAB = 60º, what is angle COE? (Note: Figure not drawn to scale.)

A. 120º
B. 135º
C. 150º
D. 165º
E. 180º
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A circle is inscribed inside a right triangle as shown. If angle CAB = 19 Jul 2020, 13:29
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Kritisood
Attachment:
Screenshot 2020-07-19 at 9.25.53 PM.png
A circle is inscribed inside a right triangle as shown. If angle CAB = 60º, what is angle COE? (Note: Figure not drawn to scale.)

A. 120º
B. 135º
C. 150º
D. 165º
E. 180º
Show more

Solution


    • The circle is inscribed in the right-angle triangle ACB.
      o Now, let us join AF.(as shown below)

      o OD, OE, and OF are radii of the inscribed circles.
         So, ∠ODA = 90°, ∠OEA = 90° and ∠OFC = 90°
    • Also, ∠CAB= ∠DAE = 60°,
      o Therefore, in quadrilateral ADOE, ∠ODA + ∠DAE + ∠OEA + ∠DOE = 360° [sum of the interior angles of a quadrilateral]
      ⟹ 90° + 60° + 90° + ∠DOE = 360°
      ⟹ ∠DOE = 120°
    • From the above diagram we have DC = OF = radius of the inscribed circle.
    • So, in triangle, CDO ,
      o DC = OD = radius of the inscribed circle.
      o Therefore, CDO is an isosceles right angle triangle.
      o Hence, ∠COD = 45°
    • Therefore ∠COE = ∠DOE + ∠COD = 120° + 45° = 165°
Thus, the correct answer is Option D.
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A circle is inscribed inside a right triangle as shown. If angle CAB = 15 Mar 2025, 10:03
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