Question

at
Secants AB and cd are intersecting at
point Q. m Carc AD)= 25°, m( are BC) 36°
then find angle Bqc​

Answer 1

Answer:

Given−

Oisthecentreofacircle.

ItschordsAB&CDintersectatQ.

m(arcAD)=25

o

andm(arcBC)=31

o

.

Tofindout−

∠BQC=?

Solution−

WejoinAD,BC&BD.

AlsowejoinAO,DO&BO,CO.

m(arcAD)=25

o

i.e∠AOD=25

o

.

Similarly

m(arcBC)=31

o

i.e∠BOC=31

o

.

Weknowthattheanglesubtendedbyachord

ofacircleatitscentreistwicetheanglesubtended

bythesamechordatitscurcumference.

∴∠BDC=

2

1

×∠BOC=

2

1

×31

o

=15.5

o

and

∠ABD=

2

1

×∠BDC=

2

1

×25

o

=12.5

o

.

∴InΔBQDwehave

∠BQD=180

o

−(∠ABD+∠BDC)=180

o

−(12.5

o

+15.5

o

)=152

o

.

∠BQC=180

o

−152

o

=28

o

(linearpair).

Ans−OptionD.

solution