Circles And Lines

Answer

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 ×…

Answer

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…

Answer

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…

Answer

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…

Answer

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…

Answer

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 …

Answer

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 …

Answer

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…