AI Geometry Solver
From basic angle rules to advanced circle theorems and 3D vectors. Upload any geometry question and get the full solution with diagrams explained.
Geometry Topics Covered
Angles & Properties of Shapes
Our solver handles angle rules for parallel lines (alternate, corresponding, co-interior angles), angle sums in polygons, properties of triangles and quadrilaterals, and bearings. It identifies which angle rules apply to the specific diagram and states each rule clearly, which is essential for earning reasoning marks at GCSE. The solver correctly uses three-letter angle notation as expected by UK examiners.
Pythagoras' Theorem & Trigonometry
From basic Pythagoras in 2D through to 3D applications, SOHCAHTOA for right-angled triangles, sine rule, cosine rule, and the area formula (half ab sin C). The solver identifies whether a triangle is right-angled and selects the most efficient approach. For non-right-angled triangles, it determines whether the sine rule or cosine rule is needed based on the known sides and angles.
Circle Theorems
All GCSE and A-Level circle theorems including the angle at the centre, angle in a semicircle, angles in the same segment, cyclic quadrilateral, tangent-radius, alternate segment theorem, and intersecting chords. The solver identifies which theorem applies from the diagram and states the theorem as a reason, exactly as mark schemes require.
Area, Volume & Surface Area
Formulae for all standard 2D shapes (rectangles, triangles, parallelograms, trapeziums, circles, sectors) and 3D solids (cuboids, prisms, cylinders, cones, spheres, pyramids, frustums). The solver selects the correct formula, substitutes values with units, and presents the final answer to the appropriate degree of accuracy. For composite shapes, it breaks the problem into manageable parts and sums or subtracts areas and volumes as needed.
Vectors
Column vectors, vector addition and subtraction, scalar multiplication, position vectors, and geometric proof using vectors. At A-Level, the solver handles 3D vectors, scalar and vector products, equations of lines and planes, and distances between points, lines, and planes. Each step in vector geometry proofs is clearly justified, showing how vector paths are constructed.
Diagram Recognition
Our AI is trained to recognise geometric diagrams from photographs, including hand-drawn diagrams from exam papers. It identifies labelled points, angle markers, parallel line arrows, and dimension annotations. This means you can photograph a question directly from a past paper or textbook and the solver will understand the geometric configuration without any manual input.