Geometric Constructions

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Step 1: Draw a circle with centre C and take a point P on the circle. Step 2: Draw ray CP. Step 3: Draw line l through P perpendicular to CP. Answer: Line l is the required tangent at P. Check: A line…

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A radius goes from the centre to the circle. At the point where it meets the circle, the tangent touches the circle only once. If the tangent were not perpendicular, it would cut the circle again near…

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Step 1: Draw the circle with centre C. Step 2: Mark point P on the circle. Step 3: Draw ray CP. Step 4: Construct a line through P perpendicular to CP. Result: The line is the tangent at P. Verificati…

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Formula: line l ⟂ CP at point P. Here, C is the centre, P is the point on the circle, and l is the tangent line. Quick use: Draw CP first, then draw the perpendicular at P. Answer check: This gives th…

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Step 1: Line CB is a chord and angle CAB is an inscribed angle. Step 2: By the tangent-secant angle theorem, angle CAB ≅ angle BCD. Step 3: By the converse of the tangent-secant theorem, if line CD is…

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Step 1: Draw a circle of suitable radius and take point C on it. Step 2: Draw chord CB and inscribed angle CAB. Step 3: With centre A and any convenient radius, draw an arc cutting the sides of angle …

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Step 1: Angle MAN and angle BCD are congruent. Step 2: Segments MN and RD are drawn equal by construction. Step 3: The other corresponding sides are matched by the same radius steps. Step 4: Therefore…

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Use the converse to confirm the final line. If line CD is drawn so that angle CAB ≅ angle BCD, then CD is the tangent. So the angle matching is not just a step; it proves the line really touches the c…