Circle Segments and Chords
📌 A chord (tali busur) is a line segment connecting two points on a circle; the arc connecting those points is the arc (busur).
📏 If two arcs are equal in length, their corresponding chords are also equal in length.

Cyclic Quadrilaterals (Segi Empat Tali Busur)
🔷 A cyclic quadrilateral is a quadrilateral whose four vertices all lie on the circle, meaning all four sides are chords.
📐 The Ptolemy's Theorem applies: The product of the diagonals equals the sum of the products of the opposite sides: $AC \cdot BD = AB \cdot CD + AD \cdot BC$.
📐 For a specific example of a kite inscribed in a circle, the area is calculated as $Area = \frac{1}{2} \cdot AC \cdot BD$. If $AB=AD=8$ and $BC=CD=13$, then $AC \cdot BD = 2(8 \cdot 13) = 208$, yielding an area of $\frac{1}{2}(208) = 100$ cm².

Angles Formed by Intersecting Chords Inside a Circle
📐 When two chords (AC and BD) intersect at point E inside a circle, the angle formed (e.g., $\angle AEB$) is half the sum of the central angles subtending the intercepted arcs: $\angle AEB = \frac{1}{2} (\angle AOB + \angle COD)$.
📐 The adjacent angle ($\angle BEC$) is half the sum of the other two central angles: $\angle BEC = \frac{1}{2} (\angle BOC + \angle AOD)$.
📐 In an example where $\angle BOC = 115^\circ$ and $\angle AOD = 41^\circ$, and $\angle AOB = 90^\circ$, the fourth central angle $\angle COD = 360^\circ - 115^\circ - 90^\circ - 41^\circ = 114^\circ$.
📐 Using the formula, $\angle AEB = \frac{1}{2} (90^\circ + 114^\circ) = 102^\circ$. The supplementary angle $\angle BEC = 180^\circ - 102^\circ = 78^\circ$.

Angles Formed by Intersecting Chords Outside a Circle
📐 When the extensions of two chords (LK and MN) intersect outside the circle at point P, the angle formed ($\angle KPN$) is half the difference between the central angles subtending the intercepted arcs: $\angle KPN = \frac{1}{2} (\angle KOL - \angle MON)$, where $\angle KOL$ is the larger central angle.
📐 In an example where $\angle KON = 94^\circ$ and $\angle MOL = 52^\circ$, the exterior angle $\angle MPL = \frac{1}{2} (94^\circ - 52^\circ) = \frac{1}{2} (42^\circ) = 21^\circ$.

Key Points & Insights
➡️ Understand the definition and properties linking equal arcs to equal chords in a circle.
➡️ Utilize Ptolemy's Theorem for calculations involving cyclic quadrilaterals, particularly relating diagonals to side lengths.
➡️ Remember the internal intersection angle rule: $\text{angle} = \frac{1}{2} (\text{sum of intercepted central angles})$.
➡️ Remember the external intersection angle rule: $\text{angle} = \frac{1}{2} (\text{difference of intercepted central angles})$.

📸 Video summarized with SummaryTube.com on Nov 18, 2025, 03:52 UTC