CBSE Class 9 Answered
Find angle x, y, r
Asked by lata15121995joshi | 03 Jan, 2020, 07:59: AM
Expert Answer
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
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