Inscribed angle
Inscribed angle is type of angle in geometry that is formed inside a circle.[1] It is made when two straight lines called chords meet at a point on the …
Inscribed angle is type of angle in geometry that is formed inside a circle.[1] It is made when two straight lines called chords meet at a point on the circle. A chord is a line segment whose endpoints lie on the circle. This means the ends of the chord touch the edge of the circle. When two chords meet at one point on the circle, they create an angle. That angle is called an inscribed angle.
The special thing about an inscribed angle is that its vertex, which is the point where the two chords meet, is on the circle itself.[1] This makes it different from other angles like central angles, where the vertex is in the middle of the circle. An inscribed angle has a very important rule: it is equal to half the measure of its intercepted arc. An arc is a part of the circle’s edge. The intercepted arc is the section of the circle that lies between the two points where the chords touch the circle.[2] So, if you know the size of the arc, you can find the size of the inscribed angle by taking half of it.[1] This relationship helps in solving geometry problems involving circles.
Inscribed angles also have other important properties. If two inscribed angles intercept the same arc or congruent arcs, then those inscribed angles are congruent, meaning they have the same size. Another important rule is that an angle inscribed in a semicircle is always a right angle, meaning it is 90 degrees and forms a perfect corner like the corner of a square.[1] There is also a rule that opposite angles formed by inscribed angles can be supplementary, meaning they add up to 180 degrees.
Inscribed angles are also related to other circle angle rules. For example, an angle formed by the intersection of two chords inside a circle is equal to half the sum of its intercepted arcs.[2] Also, an angle formed outside the circle by two secants, two tangents, or a secant and a tangent is equal to half the difference of the intercepted arcs. A tangent is a line that touches the circle at exactly one point and is perpendicular to the radius at that point. A secant is a line that intersects the circle at two points. A central angle is different from an inscribed angle because it has its vertex at the center of the circle,[2] and a central angle is equal to the measure of its intercepted arc, not half of it. Inscribed angles are useful because they help explain how circles work and how angles and arcs are connected. They are used in geometry problems involving circles, arcs, chords, tangents, and secants, helping to find missing angle measures in a simple and logical way.[2]
References
Content Disclaimer
Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.
- The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
- There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
- It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
- Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
- Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.