Question 14 Marks
Read the following text carefully and answer the questions that follow:
There was a circular park in Defence colony at Delhi. For fencing purpose poles $A, B, C$ and $D$ were installed at the circumference of the park.Ram tied wires From $A$ to $B , B$ to $C$ and $C$ to $D , $ and he managed to measure the $\angle A =100^{\circ}$ and $\angle D =80^{\circ}$
Point $O$ in the middle of the park is the center of the circle.
$i.$ Name the quadrilateral $\text{ABCD} .$
$ii$. What is the value of $\angle C$ ?
$iii$. What is the value of $\angle B$.
OR
Write any three properties of cyclic quadrilateral?
There was a circular park in Defence colony at Delhi. For fencing purpose poles $A, B, C$ and $D$ were installed at the circumference of the park.Ram tied wires From $A$ to $B , B$ to $C$ and $C$ to $D , $ and he managed to measure the $\angle A =100^{\circ}$ and $\angle D =80^{\circ}$
Point $O$ in the middle of the park is the center of the circle.
$i.$ Name the quadrilateral $\text{ABCD} .$
$ii$. What is the value of $\angle C$ ?
$iii$. What is the value of $\angle B$.
OR
Write any three properties of cyclic quadrilateral?
Answer
View full question & answer→$i. \text{ABCD}$ is cyclic quadrilateral.
A quadrilateral $\text{ABCD}$ is called cyclic if all the four vertices of it lie on a circle.
Here all four vertices $A, B, C$ and $D$ lie on a circle.
$ii$. We know that the sum of both pair of opposite angles of a cyclic quadrilateral is $180^{\circ}$.
$\angle C +\angle A =1800$
$\angle C =1800=1000=800$
$iii$. We know that
The sum of both pair of opposite angles of a cyclic quadrilateral is $180^{\circ}$.
$\angle B +\angle D =1800$
$\angle B=1800=800=1000$
OR
$I$. In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle.
$II$. The four sides of the inscribed quadrilateral are the four chords of the circle.
$III$. The sum of a pair of opposite angles is $180^{\circ} \ ($supplementary$)$.
Let $\angle A , \angle B , \angle C$, and $\angle D$ be the four angles of an inscribed quadrilateral.
Then, $\angle A +\angle C =180^{\circ}$ and $\angle B +\angle D =180^{\circ}$.
A quadrilateral $\text{ABCD}$ is called cyclic if all the four vertices of it lie on a circle.
Here all four vertices $A, B, C$ and $D$ lie on a circle.
$ii$. We know that the sum of both pair of opposite angles of a cyclic quadrilateral is $180^{\circ}$.
$\angle C +\angle A =1800$
$\angle C =1800=1000=800$
$iii$. We know that
The sum of both pair of opposite angles of a cyclic quadrilateral is $180^{\circ}$.
$\angle B +\angle D =1800$
$\angle B=1800=800=1000$
OR
$I$. In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle.
$II$. The four sides of the inscribed quadrilateral are the four chords of the circle.
$III$. The sum of a pair of opposite angles is $180^{\circ} \ ($supplementary$)$.
Let $\angle A , \angle B , \angle C$, and $\angle D$ be the four angles of an inscribed quadrilateral.
Then, $\angle A +\angle C =180^{\circ}$ and $\angle B +\angle D =180^{\circ}$.
