Tangents (Leaving Cert Mathematics): Flashcards

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Tangents
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Number of points where tangent touches circle

Exactly one point

Name of point where tangent meets circle

Point of contact

Relationship between tangent and radius at contact

Perpendicular

Number of tangents at a point on circumference

Only one (unique)

Number of tangents from external point

Two tangents

Lengths of two tangents from external point

Equal

Tangent equation at (x1,y1)(x_1, y_1) on x2+y2=r2x^2 + y^2 = r^2

xx1+yy1=r2xx_1 + yy_1 = r^2

Tangent at (x1,y1)(x_1, y_1) on (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2

(x1−h)(x−h)+(y1−k)(y−k)=r2(x_1-h)(x-h) + (y_1-k)(y-k) = r^2

Common tangents between two circles

Possible, internally or externally

Tangent to x2+y2=25x^2 + y^2 = 25 at (3,4)(3, 4)

3x+4y=253x + 4y = 25

Explore Leaving Cert Mathematics Revision Notes by Topics

The Circle

The Basics

Points Inside, Outside or On a Circle

Intersection of a Line and a Circle

Tangents & Touching Circles

Problems in g, f and c

Explore Leaving Cert Mathematics Model Answers by Topics

The Circle

The Basics

Points Inside, Outside or On a Circle

Intersection of a Line and a Circle

Tangents & Touching Circles

Problems in g, f and c

Explore Leaving Cert Mathematics Quizzes by Topics

The Circle

The Basics

Points Inside, Outside or On a Circle

Intersection of a Line and a Circle

Tangents & Touching Circles

Problems in g, f and c

Explore Leaving Cert Mathematics Exam Questions by Topics

The Circle

The Basics

Points Inside, Outside or On a Circle

Intersection of a Line and a Circle

Tangents & Touching Circles

Problems in g, f and c

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