in the given figure two circles interset at p and q if a=80degree and d=84degree calculat
Answers
Answer:
Given−
TwocirclesintersectatP&Q.
ThelinesAPB&DQCintersectthecirclesat
A,P,BandD,Q,Crespectively.
AD&BChavebeenjoined.
∠ADQ=80
o
and∠DAP=84
o
.
Tofindout−
∠QBC=?
∠BCP=?
Solution−
WejoinPQ.
ADPQisacyclicquadrilateral.
∴∠PQA=180
o
−∠ADP=180
o
−84
o
=96
o
[since
thesumoftheoppositeanglesofacyclic
quadrilateral=180
o
].
Also∠PQB=180
o
−∠PQA=180
o
−96
o
=84
o
(linearpair).
AgainQBCPisacyclicquadrilateral.
∴∠BCP=180
o
−∠BQP=180
o
−84
o
=96
o
.....(i)[since
thesumoftheoppositeanglesofacyclic
quadrilateral=180
o
].
Similarly,ADPQisacyclicquadrilateral.
∴∠QPD=180
o
−∠QAD=180
o
−80
o
=100
o
[since
thesumoftheoppositeanglesofacyclic
quadrilateral=180
o
].
Also,∠QPC=180
o
−∠QPD=180
o
−100
o
=80°
(linearpair).
AgainQBCPisacyclicquadrilateral.
∴∠QBC=180°
−∠QPC=180° −80° =100°
......(ii)[since
thesumoftheoppositeanglesofacyclic
quadrilateral=180°].
∴∠QBC=100°
and∠BCP=96°