Question

A quadrilateral is inscribed in a circle so that AB is the diameter of the circle if <ADC =105*,find m <BAC​

Answer 1

Answer:

Correct option is B)

Given:

ABCD is a cyclic quadrilateral with AB as the diameter of the circle.

Also, ∠ADC=140

o

.

We have to find: ∠BAC.

Then,

∠ADC+∠ABC=180

o

....(since the sum of the opposite angles of a quadrilateral is 180

o

).

∴∠ABC=180

o

−140

o

=40

o

.

Also, ∠ACB=90

o

....(since the angle subtended by a diameter at the circumference of the circle, is 90

o

).

∴ In ΔABC we have,

∠ACB=90

o

and ∠ABC=40

o

.

So, ∠CAB=180

o

−(∠ACB+∠ABC)

=180

o

−(90

o

+40

o

)

∴∠BAC=50

o

.

Hence, option B is correct.

Step-by-step explanation:

Please mark brainliest if it was helpful.