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Circles Practice 1: Tangents and Radius Relation

Section A: Circle and Tangent Basics

Question 1mcq
Which line touches a circle at exactly one point?
A.Tangent
B.Secant
C.Diameter
D.Chord
Question 2mcq
A line cuts a circle at two distinct points. What is it called?
A.Tangent
B.Secant
C.Radius
D.Arc
Question 3mcq
In a circle with centre OO, line PTPT touches the circle at TT. What is TT called?
A.Point of contact
B.Centre
C.Secant point
D.Midpoint of chord
Question 4mcq
Which situation correctly shows a tangent?
A.A line touches the circle at one point and does not cut through it.
B.A line passes through the centre and two points on the circle.
C.A segment joins two points on the circle.
D.A line cuts the circle at two points.
Question 5mcq
If PTPT is tangent at TT to a circle with centre OO, what is ∠OTP\angle OTP?
A.45∘45^\circ
B.60∘60^\circ
C.90∘90^\circ
D.180∘180^\circ

Section B: Radius-Tangent Theorem

Question 6mcq
Which statement is the tangent-radius theorem?
A.The tangent at any point of a circle is perpendicular to the radius through the point of contact.
B.Every chord is perpendicular to a radius.
C.A tangent always passes through the centre.
D.A secant touches the circle at one point.
Question 7mcq
In proving the tangent-radius theorem, why is the radius to the nearest point on a line important?
A.The shortest distance from the centre to the tangent line is perpendicular to the line.
B.The radius is always parallel to the tangent.
C.The tangent is a chord.
D.All radii have different lengths.
Question 8mcq
A proof says, “OTOT is a radius and PTPT is tangent, therefore OT=PTOT=PT.” What is wrong?
A.A radius is perpendicular to the tangent, not equal to the tangent length.
B.A tangent cannot touch a circle.
C.A radius is never drawn to point of contact.
D.The centre must lie on the tangent.
Question 9mcq
In a circle, OTOT is radius and PTPT is tangent at TT. If ∠OPT=35∘\angle OPT=35^\circ, find ∠POT\angle POT.
A.35∘35^\circ
B.45∘45^\circ
C.55∘55^\circ
D.90∘90^\circ
Question 10mcq
A student sees a tangent and radius at the point of contact and marks the angle as 80∘80^\circ. What is the misconception?
A.The angle must be 90∘90^\circ.
B.The angle must equal the radius.
C.A tangent creates no angle.
D.The radius must be parallel to tangent.