Question

दी गई आकृति मे AB व्यास है और केंद्र बिंदु o है । यदि < COD = 40 • है तो CEDज्ञात कीजिए ।​

Answer 1

Given : आकृति मे AB व्यास है और केंद्र बिंदु O है . ∠COD = 40°

To find :  ∠CED

Solution:

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  + ∠COD

=> ∠OAC + ∠BDO  + ∠COD = 180°

=> x  +  y + ∠COD = 180°

=> ∠COD = 180° - x - y

∠COD = ∠CDO    as ( OC = OD  = Radius)

=> ∠COD = 180° - x - y

in ΔOCD

∠DCO + ∠COD + ∠DOC=  180°

=> 2 ( 180° - x - y)  + 40° = 180°

=>  180° - x - y = 70°

in ΔAEB

∠EAB + ∠EBA  + ∠AEB = 180°

∠AEB  = ∠CED

=> x + y + ∠CED = 180°

=>∠CED = 180° - x - y

=> ∠CED = 70°

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