In a circle with centre o, ac and bd are two chords. Ac and bd meet at e when produced. If ab is the diameter and aeb=68, then the measure of doc is? ,d o dsunz okys o`k esa] ac vksj bd nks thok, gsaa tc
Answers
∠DOC= 44° if AC & DB are two chords and meet at E , AB is Diameter & ∠AEB = 68°
Step-by-step explanation:
Lets join OC & OD
now in Δ AOC
OA = OC ( Radius)
=> ∠CAO = ∠ACO = x
Simialrly
∠DBO = ∠BDO = y ( as OD = OB = Radius)
ABCD is a cylic Quadrilateral
=> ∠BAC + ∠BDC = 180° ( oposite angles)
∠BAC = ∠OAC as O lies on AB ( as AB is diameter)
∠BDC = ∠BDO + ∠CDO
=> ∠OAC + ∠BDO + ∠CDO = 180°
=> x + y + ∠CDO = 180°
=> ∠CDO = 180° - x - y
∠DCO = ∠CDO as ( OC = OD = Radius)
=> ∠DCO = 180° - x - y
in ΔAEB
∠EAB + ∠EBA + ∠AEB = 180°
=> x + y + 68° = 180°
=> 68° = 180° - x - y
=> ∠DCO = ∠CDO = 68°
in ΔOCD
∠DCO + ∠CDO + ∠DOC= 180°
=> 68° + 68° + ∠DOC= 180°
=> ∠DOC= 44°
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