ABC is a triangle

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ABC is a triangle

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Enhanced PromptConstructing triangle ABC with given side lengths AB = 90 mm, AC = 80 mm, and angle CAB = 75°, triangle ABC is an oblique triangle, detailed construction steps, using a ruler and protractor to draw the sides and angles accurately, draw line segment AB of length 90 mm, at point A, draw a ray AX such that angle BAX = 75°, with center A and radius 80 mm, draw an arc to cut ray AX at point C, join BC to form triangle ABC, triangle ABC has the required measurements. To complete quadrilateral ABDC, where AD = DC = 65 mm, at point A, draw an arc with radius 65 mm to cut line AC extended at point D, with center D and radius 65 mm, draw an arc to cut line BC extended at point C, join AD, DC, and CB to form quadrilateral ABDC, ABDC is the required quadrilateral. To construct the inscribed circle for triangle ADC, let the center of the inscribed circle be I, and the radius be r, draw the angle bisectors of angles A and C to intersect at point I, from point I, draw a perpendicular line to side AC to meet AC at point E, join IE, line segment IE is the radius of the inscribed circle, place the point of the compass at point I and draw a circle with radius IE to intersect sides AD, DC, and AC at points F, G, and E, respectively, the circle with center I and radius r is the inscribed circle of triangle ADC, triangle ADC with an inscribed circle is the final construction. The detailed diagram shows triangle ABC with the given measurements, quadrilateral ABDC with AD = DC = 65 mm, and the inscribed circle of triangle ADC with center I and radius r, each step of the construction is accurately drawn using a ruler and protractor, the final diagram is a precise representation of the given problem. The diagram is drawn in a 2D plane, with a clear and concise layout, the triangle, quadrilateral, and inscribed circle are accurately constructed, the diagram is well-labeled, with each point and line segment clearly marked, the construction steps are easy to follow, and the final diagram is a accurate representation of the problem. The diagram is a masterpiece of technical drawing, with precise lines, angles, and curves, the use of a ruler and protractor ensures accuracy and precision, the diagram is a testament to the importance of attention to detail and technical skill in drawing and construction. The style of the diagram is reminiscent of classic technical drawing, with a focus on precision and accuracy, the use of simple lines and curves creates a clean and uncluttered diagram, the diagram is easy to read and understand, with each element clearly labeled and marked. The diagram is a work of art, with a beauty and elegance that is both pleasing to the eye and informative, the use of color and shading adds depth and dimension to the diagram, the diagram is a masterpiece of technical drawing and a testament to the importance of precision and accuracy in drawing and construction.

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