Angle in a Circle

MathematicsCircle GeometryEasy

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The image shows a geometric diagram of a circle with center $O$. The arc $AB$ has a measure of $46^{\circ}$. The central angle $\angle AOB = x$ and the inscribed angle $\angle ACB = 23^{\circ}$. It is demonstrated that $x = 46^{\circ}$.

This question includes visual content: A circle with center O. Points A, B, and C are on the circumference. An arc AB has a measure of 46 degrees. The central angle AOB is marked as x. An inscribed angle ACB is marked as 23 degrees. Lines connect O to A and O to B, and lines connect C to A and C to B. The text 'x = 46' is written to the right of the circle.

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Step by Step Written Solution

1
Step 1

Merhaba Aliosman, bu çember sorusunu seninle adım adım çözelim.

Çemberde Açılar

2
Step 2

Şekle baktığımızda, çember üzerinde bir çevre açımız ve bir merkez açımız olduğunu görüyoruz. İlk olarak verileri temiz bir çizimle görelim.

OABC23°
3
Step 3

C noktasındaki yirmi üç derecelik açı bir çevre açıdır. Çevre açının kuralına göre, gördüğü yayın ölçüsü açının iki katına eşittir.

$$m(\text{Yay } AB) = 2 \times m(\widehat{ACB})$$
4
Step 4

Buradan, AB yayının ölçüsünü iki çarpı yirmi üçten kırk altı derece olarak buluruz.

46°

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About This Question

Subject
Mathematics
Topic
Circle Geometry
Difficulty
Easy

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