We have studied that a quadrilateral is a 4 – sided polygon with 4 angles and 4 vertices. For more details, you can consult the article “Quadrilaterals” in the “Polygon” section.
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In geometry exams, examiners make the questions complex by inscribing a figure inside another figure and ask you to find the missing angle, length, or area. One example from the previous article shows how an inscribed triangle inside a circle makes two chords and follows certain theorems.
This article will discuss what a quadrilateral inscribed in a circle is and the inscribed quadrilateral theorem.
What is a Quadrilateral Inscribed in a Circle?
In geometry, a quadrilateral inscribed in a circle, also known as a cyclic quadrilateral or chordal quadrilateral, is a quadrilateral with four vertices on the circumference of a circle. In a quadrilateral inscribed circle, the four sides of the quadrilateral are the chords of the circle.
Solution
Sum of 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 sides 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 on both sides,
x = 18 o
Substitute.
(3x – 2) o ⇒ 52 o
(7x + 2) o ⇒ 128o
Practice Questions
1. All polygons can be inscribed in a circle.
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A. Yes
B. No
2. Inscribed quadrilaterals are also 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 the opposite angles are ______