Question

in the figure c is the centre of circle and angle ABD=30° what is the measure of ACD
​

Answer 1

Step-by-step explanation:

ANSWER

(a) The angle made by an arc at any point on the alternate arc is equal to half the angle made at centre.

∴m∠ABD=

2

1

m∠ACD

∴m∠ACD=60

o

(b)∠ABD=∠CAB

∴∠CAB=30

o

In △CAE,∠ACE+∠CAE+∠CEA=180

o

60

o

+30

o

+∠CEA=180

o

∠CEA=90

o

∴CE is perpendicular to the chord AB.

A perpendicular drawn from the centre of the circle to the chord bisects the cord.

∴AE=EB=

2

1

AB=3cm

In △CAE,sinC=

AC

AE

∴sin60

o

=

AC

3

∴AC=3×

3

2

=2

3

cm

Hence, radius of the circle is 2

3

cm.

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