Circles And Lines — Flashcards

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When two chords of a circle intersect within the circle, the product of the parts of one chord equals the product of the parts of the other chord. If chords AB and CD intersect at point P, then: AP ×…

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Step 1: Apply the intersecting chords theorem AP × PB = CP × PD Step 2: Substitute known values 6 × 4 = 3 × PD 24 = 3 × PD Step 3: Solve for the unknown segment PD = 24 ÷ 3 = 8 cm Therefore, the ot…

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When a diameter of a circle is cut by a perpendicular chord, the product of the parts of the diameter equals the square of half the perpendicular chord. If parts of diameter = a and b, and half-chord…

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Step 1: Apply the perpendicular chord theorem Product of diameter segments = (half-chord)² 3 × 2 = c² Step 2: Calculate 6 = c² c = √6 cm Step 3: Find full chord length Full chord = 2c = 2√6 cm Ther…

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Step 1: Draw a line segment of length 6 cm Step 2: Mark point P such that AP = 2 cm and PB = 3 cm (so 2 × 3 = 6) Step 3: At P, draw a perpendicular line Step 4: Draw a semicircle with AB as diameter S…

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For a circle with radius r and point P at distance d from center: If P is INSIDE the circle: PX × PY = r² - d² If P is OUTSIDE the circle: PX × PY = d² - r² General form: PX × PY = |r² - d²| Where …

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Step 1: Identify the given information Radius r = 3 cm, Distance d = 5 cm Since d > r, point P is OUTSIDE the circle Step 2: Apply the formula for external point PX × PY = d² - r² Step 3: Calculate …

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For a point P outside a circle: PX × PY = PT² Where: - X, Y are intersection points of any secant through P - T is the point of tangency from P to the circle - PT is the tangent length This means: T…