Math, asked by abhishek6712, 4 months ago

in the given figure two circles interset at p and q if a=80degree and d=84degree calculat​

Answers

Answered by tecnicgaming1133
2

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°

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