chords AB and CD of a circle intersect in point Q in the interior of a circle if m(arc AD)=25 and m(arc BC)=31 find angle BQC
Answers
Answered by
8
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
Answered By
toppr
159 Views
How satisfied are you with the answer?
This will help us to improve better
answr
Get Instant Solutions, 24x7
No Signup required
girl
Similar questions