Constructions — Part 1: Tangents from an external point: visual lesson, ICSE Class 10 Mathematics

Lesson

Tangents from a point: construction

A tangent touches a circle at exactly one point. From a point outside a circle you can draw two tangents, and with ruler and compasses you can construct them exactly.

In this lesson you will

State that a tangent is perpendicular to the radius at the point of contact
Construct the two tangents from an external point to a circle, with steps of construction
Calculate the length of a tangent and the angle between two tangents, and check against measurement
Solve problems on concentric circles and on tangents inclined at a given angle

Two tangents from $P$ to a circle of radius $3$ cm: $PA = PB = 4$ cm. Lengths in cm.

Concept

What you will be able to do

Use the right angle between a tangent and a radius
Follow and write the steps of construction of the tangents
Find the length of a tangent and the angle between two tangents
Handle concentric circles and tangents at a given angle

Concept

A tangent and the radius to its point of contact

A tangent meets the circle in one point $T$ , the point of contact. The radius $OT$ is perpendicular to the tangent, and every other point of the tangent lies outside the circle.

the tangent at $T$ is the only line through $T$ that does not enter the circle
from a point inside the circle no tangent can be drawn

OT \perp \text{tangent at } T

A tangent touches the circle at one point $T$ and is perpendicular to the radius $OT$; every other point of it is outside. Length in cm.

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