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Find angle x, y, r
Asked by lata15121995joshi | 03 Jan, 2020, 07:59: AM
In triangle OEC,
angle OEC + angle OCE + angle EOC = 180
90 + 30 + angle EOC = 180
angle EOC = 60 ...(i)

In triangle OBC,
OB = OC                   radii of the same circle
angle OBC = angle OCB = 30     opposite angles of equal sides
In triangle OEC,
angle OEC + angle OBC + angle BOC = 180
90 + 30 + angle BOC = 180
angle BOC = 60 ...(ii)

AE is straight line.
Hence,
angle BOC + angle BOA = 180
60 + angle BOA = 180               from (ii)
angle BOA = 120

In triangle OAB,
OA = OB                     radii of the same circle
angle OAB = angle OBA = x       opposite angles of equal sides
In triangle OAB,
angle OAB + angle OBA + angle AOB = 180
x + x + 120 = 180
2x = 60
x = 30

2angle DC=arc DC             inscribed angle theorem

angle DOC = arc DC          central angle
Hence, angle DOC = 2angle DBC = 2y

We know that
angle AOD + angle DOC + angle COE = 180                 AE is diameter and straight line
90 + 2y + 60 = 180
2y = 60
y = 30

Answered by Sneha shidid | 06 Jan, 2020, 10:38: AM

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