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A circle is inscribed inside a right triangle as shown. If angle CAB =

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Kritisood
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A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink] New post   Updated on: 19 Jul 2020, 09:03
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Screenshot 2020-07-19 at 9.25.53 PM.png [ 20.11 KiB | Viewed 2592 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

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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Re: A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink] New post   19 Jul 2020, 09:00
Kritisood wrote:
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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Re: A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink] New post   19 Jul 2020, 09:04
chipsy wrote:
Kritisood wrote:
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


apologies, corrected the question.
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Re: A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink] New post   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 wrote:
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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Re: A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink] New post   19 Jul 2020, 13:29
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Kritisood wrote:
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


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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Re: A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink] New post   26 Jul 2021, 08:45
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Re: A circle is inscribed inside a right triangle as shown. If angle CAB = [#permalink]
26 Jul 2021, 08:45
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