Write the correct answer in the following: ABCD is a cyclic quadr… - Vidyadip

MCQ

Write the correct answer in the following: $ABCD$ is a cyclic quadrilateral such that $AB$ is a diameter of the circle circumscribing it and $\angle\text{ADC}=140^\circ,$ then $\angle\text{BAC}$ is equal to:

A
$80^\circ .$
✓
$50^\circ .$
C
$40^\circ .$
D
$30^\circ .$

✓

Answer

Correct option: B.

$50^\circ .$

Given, $ABCD$ is a cyclic quadrilateral and $\angle\text{ADC}=140^\circ.$

We know that, sum of the opposite angles in a cyclic quadrilateral is $180^\circ .$
$\angle\text{ADC}+\angle\text{ABC}=180^\circ$
$\Rightarrow\ 140^\circ+\angle\text{ABC}=180^\circ$
$\Rightarrow\ \angle\text{ABC}=180^\circ-140^\circ$
$\therefore\angle\text{ABC}=40^\circ$
Since, $\angle\text{ACB}$ is an angle in a semi-circle.
$\therefore\angle\text{ACB}=90^\circ$
In $\triangle\text{ABC},\ \ \angle\text{BAC}+\angle\text{ACB}+\angle\text{ABC}=180^\circ$ [by angle sum property of a triangle]
$\Rightarrow\angle\text{BAC}+90^\circ+40^\circ=180^\circ$
$\Rightarrow\angle\text{BAC}=180^\circ-130^\circ=50^\circ$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Circles→Circles — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

In Fig , if $\triangle A B C$ is an isosceles triangle with $A B=A C$ and $B D=C D$, then the congruence criterion by which $\triangle A D B \cong \triangle A D C$ is

The graph of the linear equation y = x passes through the point

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is:

The things which are double of same things are:

$x = 2, y = -1$ is a solution of the linear equation:

In Fig. which of the following statements must be true?
(i) a+b=d+c$\quad$(ii) $a+c+e=180^{\circ}$$\quad$(iii) b+f=c+e

If $r$ is the radius and $h$ is height of the cylinder the volume will be:

Which one of the following is a polynomial$?$

Two chords $AB$ and $CD$ of a circle intersect each other at a point $E$ outside the circle. If $AB = 11\ cm, BE = 3\ cm$ and $DE = 3.5\ cm,$ then $CD = ?$

If a linear equation has solutions (-2, 2) (0, 0) and (2,2), then it is of the form