Tangents and Secants to a Circle

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Step 1: Check the number of common points. Step 2: If there is no common point, the line does not meet the circle. Answer: It is a non-intersecting line with respect to the circle.

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Step 1: The line meets the circle at two points. Step 2: A line meeting a circle at two points is a secant. Step 3: The segment joining the two points of intersection is a chord. Answer: The line is a…

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Step 1: Count the common points. Step 2: Exactly one common point means the line touches the circle. Answer: The line is a tangent, and A is the point of contact.

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A secant cuts a circle at two distinct points. If those two points of intersection come together into one point, the secant becomes a tangent. So a tangent is a special case of a secant where the two …

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Use it when a tangent is drawn at a point on a circle and the radius to that point is known. Worked example: If XY is tangent at P and O is the centre, then OP is perpendicular to XY. So angle OPX = …

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Formula: OP ⟂ XY Here, OP is the radius through the point of contact P, and XY is the tangent. Quick example: If a radius meets a line at the point of contact, that line forms a right angle with the r…

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Step 1: Assume Q is another point on the tangent line XY. Step 2: If Q were inside the circle, then XY would cut the circle at two points. Step 3: That would make XY a secant, not a tangent. Answer: Q…

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Step 1: Since OA is a radius and PA is tangent, angle OAP = 90°. Step 2: Use Pythagoras theorem in triangle OAP: OP^2 = OA^2 + PA^2 Step 3: Substitute values: 10^2 = 6^2 + PA^2 100 = 36 + PA^2 Step 4:…