Opening your next discovery…
How much evidence fixes the centre of a circle?
Your discovery goalConstruct a circumcentre from two independent perpendicular bisectors and distinguish non-collinear, collinear and coincident point constraints.
Mapping checkedA prediction is a starting idea. You can revise it after exploring.
Use at least 40 characters and include an observation. Your writing is saved as evidence; it is not automatically judged for accuracy.
This records completion of this demonstration. It is not an official grade or a claim of mastery.
Construct independent chord bisectors, compare equal radii and test a report whose three rim marks become collinear.
Construct a circumcentre from two independent perpendicular bisectors and distinguish non-collinear, collinear and coincident point constraints.
State what you changed. Describe the result using an observation from the model. Connect the observation to the idea you are learning, then try a different case to test your explanation.
Build on what you know. Discover where it leads.
Open the learning mapCurrent syllabus body inspected; unique circumcircle and construction outcomes crosswalked to the current Ganita Manjari chapter title, not substituted for it.
Current body inspected. Original circumcentre construction and degeneracy tasks; wider chord/angle outcomes and the whole IX crosswalk remain separate. SHA and page-level audit in BATCH3-SECONDARY-MATH-SOURCES.md.
Mapping scope: Original exact two-dimensional schematic. Numerical agreement illustrates a geometric argument; samples alone are not a universal proof. A finite circle requires three distinct non-collinear marks. A repeated/coincident bisector adds no independent constraint. Coordinates scaffold construction, not a new vector curriculum.
The explanations, models and assessments on labs.bodhiclasses are original learning activities. An official reference establishes curriculum context; it does not imply approval of this activity by CBSE or NCERT.
Investigation 01 · geometric reconstruction
A circular display wheel has lost its centre mark. Three distinct rim marks A, B and C remain. Build geometric constraints before proposing a replacement centre. Coordinates are original schematic units, not measurements of a real wheel.
A (−4, 0), B (4, 0). Exact schematic, equal scale on both axes. A circle through A alone is only a candidate.
Rim marks use whole-number grid coordinates from −20 to 20; candidate centres may be fractional and range from −1000 to 1000. Changing a rim mark clears the previous construction. Coincident or collinear marks are allowed as diagnostic cases, not accepted as a unique circle.
No constructed constraints yet. A chord’s midpoint belongs on its perpendicular bisector; the centre must also lie somewhere on that line.
0 retained constructions; two independent intersecting lines still needed.
Candidate distances: OA = 4, OB = 4, OC = 8 units. Equal values support the observed fit; the bisector argument explains it.
Investigation 02 · challenge the conditions
A second report places all three distinct rim marks on one straight line. Can those exact marks belong to a finite circle, or does the report contradict the circular-wheel model?
A and B stay fixed. The transfer diagram displays the AB and AC bisectors when each chord has distinct endpoints.
Original exact 2D construction mapped to current NCERT IX Ganita Manjari §5.3. Candidate coordinates are accepted within 0.001 units, so three decimal places suffice for a recurring centre coordinate; displayed distances use three decimal places. Numerical agreement illustrates the construction; the geometric equidistance argument supplies the explanation. This mission covers circumcentre construction and degeneracy, not the chapter’s complete chord/arc/angle theory. Coordinates and keyboard controls are construction aids; progress stays browser-local.
