We have actually studied the a square is a 4 – sided polygon through 4 angles and 4 vertices. For much more details, you can consult the post “Quadrilaterals” in the **“Polygon” section.You are watching: Which property is always true for a quadrilateral inscribed in a circle?**

In **geometry exams**, assessors make the questions complicated by inscribing a number inside another figure and ask you to find the absent angle, length, or area. One example from the previous article shows how an inscriptions triangle within a circle makes two chords and also follows particular theorems.

This write-up will talk about what a quadrilateral inscribed in a circle is and the inscribed quadrilateral theorem.

## What is a quadrilateral Inscribed in a Circle?

**In geometry, a square inscribed in a circle, likewise known as a cyclic square or chordal quadrilateral, is a square with four vertices on the one of a circle. In a quadrilateral inscribed circle, the four sides the the quadrilateral are the chords the the circle.**

Solution

Sum that opposite angles = 180 o

(y + 2) o + (y – 2) o = 180 o

Simplify.

y + 2 + y – 2 =180 o

2y = 180 o

Divide by 2 on both political parties to get,

y = 90 o

On substitution,

(y + 2) o ⇒ 92 o

(y – 2) o ⇒ 88 o

Similarly,

(3x – 2) o = (7x + 2) o

3x – 2 + 7x + 2 = 180 o

10x =180 o

Divide by 10 ~ above both sides,

x = 18 o

Substitute.

(3x – 2) o ⇒ 52 o

(7x + 2) o ⇒ 128o

*Practice Questions*

1. Every polygons deserve to be enrolled in a circle.

See more: Advantages Of Post & L In Post And Lintel Construction Stone Usually

A. Yes

B. No

2. Inscriptions quadrilaterals are likewise called _____

A. Trapped quadrilaterals

B. Cyclic quadrilaterals

C. Tangential quadrilaterals

D. None of these.

3. A quadrilateral is inscribed in a circle if and only if opposing angles room ______