Compute missing circle measures from right triangle relationships. Review formulas, examples, and clean plotted visuals. Download results quickly for study, teaching, or practice needs.
Enter exactly two independent values. The calculator solves the rest using the Pythagorean theorem and chord relations.
This graph shows the circle, chord, center distance, and right triangle used in the calculation.
| Case | Radius (r) | Center Distance (d) | Half Chord (a) | Full Chord (c) | Central Angle |
|---|---|---|---|---|---|
| Example 1 | 10 | 6 | 8 | 16 | 106.26° |
| Example 2 | 13 | 5 | 12 | 24 | 134.76° |
| Example 3 | 15 | 12 | 9 | 18 | 73.74° |
| Example 4 | 9 | 8.4853 | 3 | 6 | 38.94° |
The key geometric model comes from a radius drawn to the midpoint of a chord. That radius, the perpendicular center distance, and half the chord form a right triangle.
Here, r is radius, d is the center-to-chord distance, a is half chord, c is full chord, and θ is the central angle in radians.
It solves missing circle measures created by a chord and a perpendicular line from the center. It also returns angle, arc length, sector area, and a theorem check.
Enter any two independent values among radius, center distance, half chord, and full chord. Valid pairs include radius with chord, radius with distance, or distance with chord.
Those two values are directly dependent because full chord equals twice the half chord. They do not provide enough geometric information to determine the radius or center distance.
Yes. A zero center distance means the chord passes through the center, so the chord becomes a diameter. The right triangle then becomes a special limiting case.
The most common reason is inconsistent values. For example, a chord cannot be longer than the diameter, and a half chord cannot be larger than the radius.
It is the angle formed at the center by the two radii that connect the circle’s center to the chord’s endpoints. It helps determine arc length and sector area.
The graph makes the right triangle inside the circle easier to understand. It visually confirms the relationship between radius, center distance, and half chord before or after solving.
Yes. It is useful for homework checks, geometry revision, and quick theorem verification. The result table and exports also help organize worked examples for later review.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.