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

Given:

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

Also, ∠ADC=140o. 

We have to find: ∠BAC.

Then, 

∠ADC+∠ABC=180o ....(since the sum of the opposite angles of a quadrilateral is 180o).

∴∠ABC=180o−140o=40o. 

Also, ∠ACB=90o  ....(since the angle subtended by a diameter at the circumference of the circle, is 90o).

∴ In ΔABC we have,

∠ACB=90o and ∠ABC=40o. 

So, ∠CAB=180o−(∠ACB+∠ABC)

=180o−(90o+40o)

∴∠BAC=50o .

❥︎THANKS

I hope it will help you.