Miss, cut or touch
Only three possibilities
A line and a circle share no point, two points, or exactly one.
↳ There is no fourth case.
📚 Chapter Learning Kit
Circles · Class 10 Mathematics
English 2 topics 114 leveled MCQs 44 flashcards 2 games Free
Shared by a Veda teacher · Generated with Veda AI · Sep 2026
⚡ Veda Bites
💡 Key Idea
➗ Formula
💡 Key Idea
💡 Key Idea
⚙️ Process
⚠️ Common Mistake
The whole idea, one bite at a time
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Point of contact
The single meeting place
The one point a tangent shares with its circle.
↳ Every theorem in this chapter lives at that point.
The tangent as a limit
A secant that ran out of room
Slide a secant outwards and its two crossing points move together.
↳ A tangent is a secant with its points merged.
Theorem 2
Exactly two, and equal
From a point outside a circle, exactly two tangents can be drawn.
↳ The equality is what makes tangent figures tractable.
The three ingredients
Why they must be equal
↳ Right angle, Hypotenuse, Side — RHS.
Naming the criterion
Not SSS, not SAS
Only two sides are known equal at the start, and the equal angle is not between them.
↳ Say RHS explicitly.
📖 Smart notes
What you'll study, topic by topic
1
The Tangent to a Circle
A line and a circle can meet twice, once, or not at all. The 'once' case is the tangent, and everything in this chapter follows from one fact about it: the radius drawn to the point of contact meets it at a right angle.
- A SECANT cuts a circle at TWO points; a TANGENT touches it at exactly ONE.
- The single common point is called the POINT OF CONTACT.
- THEOREM 1: the tangent at any point of a circle is perpendicular to the radius through the point of contact.
~45 min · full explanation, examples & memory tricks in the app
2
Tangents from an External Point
From a point outside a circle exactly two tangents can be drawn, and they are always equal in length. That single fact turns a great many circle figures into simple sums.
- THEOREM 2: the lengths of the two tangents drawn from an external point to a circle are EQUAL.
- The proof uses the RHS congruence of the two right triangles formed.
- The right angles come from Theorem 1, the equal radii from the definition of a circle, and the common hypotenuse from the shared segment…
~50 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
114 questions laddered from warm-up to topper-level, each with an explanation. A taste:
A line meeting a circle at two points is called a
Beginner
A tangent
B radius
C secant
D diameter
Show answer & explanation
secant
It cuts through.
A line meeting a circle at exactly one point is called a
Beginner
A secant
B chord
C diameter
D tangent
Show answer & explanation
tangent
It touches.
The single point a tangent shares with its circle is the
Beginner
A centre
B point of contact
C midpoint
D vertex
Show answer & explanation
point of contact
That is its name.
The greatest number of points a straight line can share with a circle is
Beginner
A one
B three
C two
D unlimited
Show answer & explanation
two
A secant is the extreme case.
🃏 Flashcards
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44 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
Play your way through this kit
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
True False
Playable in the app
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