Question

if two circles intersect in C and D point.Two line through the point D and C intersect the circle in A and B point and another circle in E and F point .If angle DAB=75 DEGREE then find angle DEF

Answer 1

Answer:

D

(i) 68

o

, (ii) 96

o

∠DEF=110

o

∠ACB=32

o

∠DAB=118

o

ABCD and CDEF are cyclic quadrilateral

∠BAD+∠BCD=180

o

118+∠BCD=180

∠BCD=62

∠BCA+∠ACD=62

32+∠62

∠ACD=30

In ABCD cyclic quadrilateral

∠BCA=∠BDA

∠BDA=32

o

(angle in major sector from same chord)

∠BDA=∠EDF=32

o

(opposite angle)

In △DEF

∠DEF+∠EDF+∠DFE=180

∠DFE=180−32−110=38

o

∠DFE=∠DCE=38

o

(angle in major segment from same chord)

i)∠ACE=∠ACD+∠DCE=30+38=68

o

ii)∠COD=96

o