In the given figure O is the centre of the circle ∠=30°,find x, y and z.
Answers
Answer:
Given−
BA, BD & BC are the chords of the circle with
centre O.
AE⊥BC & OD⊥AE.
∠OCE=30
o
.
To find out−
∠BAE=x=? And ∠DBC=y=?
Solution−
We join AD & DC.
∠ABD=
2
1
∠AOD=
2
1
×90
o
=45
o
.
(∵ The angle at the centre of a circle subtended by a chord
is double of that at the circumference.).
∴ In ΔOEC we have ∠COE=180
o
−(∠OEC+∠OCE)=180
o
−(90
o
+30
o
)=60
o
.
(angle sum property of triangles)
∴ ∠DOC=∠DOE−∠COE=90
o
−60
o
=30
o
.
Now ∠DBC=y=
2
1
∠DOC=
2
1
×30
o
=15
o
.
(∵ The angle at the centre of a circle subtended by a chord
is double of that at the circumference.).
Again ∠ABE=y+45
o
=45
o
+15
o
=60
o
.
∴ In ΔABE we have ∠BAE=x=180
o
−(∠ABE+∠AEB)=180
o
−(60
o
+90
o
)=30
o
.
(angle sum property of triangles)
So x=30
o
& y=15
o
.