Inscribed Angle Theorems Proof | Inscribed Angle Theorem Formula

What is Inscribed Angle Theorems?

In Geometry, the inscribed angle is formed in the interior of a circle with two secant lines intersecting on the circle. Or this could be taken as the angle subtended at a specific point on the circle by two other points. In brief, an inscribed angle is defined by two chords of the circle sharing an endpoint.

The inscribed angle theorem is related to the measure of an inscribed angle to the central angle subtending over the same arc. The theorem states that an inscribed angle θ in the circle is half of the central angle i.e. 2θ subtends over the same arc on the circle. This is the reason why the angle

Inscribed Angle Theorem

The use inscribed angle is pretty common when you study geometry during your early schools or colleges. One special case of the Theorem is the Thales’ Theorem that states that the angle subtended by a diameter would always be 90-degree that is a right angle. If you are taking the consequence of the theorem then the sum of opposite angles of a cyclic quadrilateral would result in 180-degrees.

Conversely, any Quadrilateral for which this condition is true can be inscribed within a circle. This theorem would act as the baseline for many other theorems as frequently used by students with respect to the circle. It will allow the intersection of two chords within a circle and the products of the length of their pieces is almost equal.

According to the Inscribed Angle Theorems in the mathematics, the inscribed angle (A) is half the central angle (C)Circle Theorems. It can also be written as A = C / 2 mathematically or C = 2A. this hardly counts in terms of logic but easy to remember. So, you choose your best way to memorize the theorem in your own style.

Inscribed Angle Theorem Formula

Circles are used everywhere around and inscribed angles are the special angles that sits within a circle on the vertex, on the circumference of the circle. This is true that every inscribed angle shares a special relationship with the intercepted arc. The vertex is defined as the common endpoint of two sides of the angle and the sides are named as the chord of a circle. The chord is the line segment who endpoints also sit on the circumference of a circle.

One of the endpoints is named as the vertex and another endpoint sits across the circle. The arc formed by the inscribed angle is named as the intercepted arc formed between two chords of angle and intersected by the chords too. The intercepted angle and the intercepted arc always share a special relationship. Here, in the figure below, you can see how to define the inscribed angle, vertex, and the chord in the Geometry.

Here, in the example, the intercepted arc is measured as 48-degree and the inscribed angle would be the half of the intercepted arc i.e. 24-degrees.


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