Buffyyour study buddyHi! Ask me why a tangent is perpendicular to the radius, or how to find a tangent's length.
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A tangent grazes a circle at a single point — and it always meets the radius there at a perfect right angle. Two tangents from the same outside point are always equal. Drag the point and see both laws hold.
Play with it
Move the external point P nearer or further. The two tangents PA and PB stay equal (length √(OP² − r²)), and each meets its radius at a right angle.
Learn
A tangent is a line that touches a circle at exactly one point — the point of contact. A secant cuts across the circle at two points.
How many tangents you can draw depends on where you stand:
Theorem: the tangent at any point of a circle is perpendicular to the radius drawn to the point of contact.
Because the angle is 90°, the radius, the tangent and the line to an external point form a right triangle — so you can use Pythagoras to find lengths.
A point P is 13 cm from the centre of a circle of radius 5 cm. Find the length of the tangent from P.
Theorem: the lengths of the two tangents drawn from an external point are equal. Also, the line from the centre to that point bisects the angle between the tangents.
Two tangents PA and PB are drawn from an external point P. If PA = 7 cm, find PB.
For a quadrilateral whose four sides all touch a circle, opposite sides add up equally: AB + CD = AD + BC (it falls straight out of equal tangents).
Why this matters
"Tangent" sounds abstract until you notice it everywhere a wheel meets a road, a belt wraps a pulley, or a road curves smoothly into a bend.
A wheel touches the road at exactly one point, and the spoke (radius) there is perpendicular to the road (tangent) — that right angle is why a wheel rolls cleanly. Conveyor belts and bike chains run along the common tangents of their pulleys and gears.
Tangent ⊥ radiusWhen a straight road curves into a bend, engineers join the straight part to a circular arc tangentially — meeting at a tangent — so the steering changes smoothly with no sudden jerk. Railway curves and skateboard ramps use the same idea.
Smooth tangent joinsThe farthest point a satellite can see is along a tangent to the Earth — that sets its coverage.
Engineers compute belt length from the common tangents between two pulleys.
Light grazing a curved surface and tangent lines define where reflections and glints appear.
Satellite coverage, belt design, optics and more — each explained with a diagram. Free to unlock.
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Modelled on CBSE's competency pattern — MCQ, assertion–reason and case-study items.
Interactive visualiser hand-built for trykarkedekho. Content from the rationalised NCERT Class 10 Maths syllabus (ncert.nic.in).
Buffyyour study buddyBuffy is an AI helper and can be wrong — always check your NCERT textbook.