Math, asked by ranjanasri749, 2 months ago

In the given figure O is the centre of the circle ∠=30°,find x, y and z.

Answers

Answered by vishalchoudharyo126
3

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

.

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