Vidaara.orgClass 10 · Mathematics
CodeVID-M10-08-PRP-01
Properties of Tangents — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The tangent is ___ to the radius at the point of contact.
- A.parallel
- B.perpendicular
- C.equal
- D.oblique
2.
Tangents from an external point are:
- A.unequal
- B.equal
- C.perpendicular
- D.parallel
3.
The angle between tangent and radius at the contact point is:
- A.$45^\circ$
- B.$90^\circ$
- C.$60^\circ$
- D.$30^\circ$
4.
If $PA,PB$ are tangents from $P$, then:
- A.$PA=PB$
- B.$PA>PB$
- C.$PA
- D.$PA=2PB$
5.
The tangent $\perp$ radius theorem is used to prove:
- A.equal areas
- B.right angles
- C.parallel lines
- D.equal angles
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
State the tangent–radius theorem.
7.
If $PA$ and $PB$ are tangents from $P$ and $PA=6$, find $PB$.
8.
What is the angle between a tangent and the radius at the contact point?
9.
State the property of the lengths of two tangents from an external point.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
$PA$ and $PB$ are tangents from $P$ to a circle with centre $O$. If $\angle APB=60^\circ$, find $\angle AOB$.
11.
A tangent $PT$ touches a circle of radius $6$; if $OP=10$, find $PT$.
12.
If tangents $PA,PB$ from $P$ subtend $\angle AOB=110^\circ$ at the centre, find $\angle APB$.
13.
State why the lengths of tangents from an external point are equal.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Two tangents $TP$ and $TQ$ are drawn from an external point $T$ to a circle with centre $O$. Prove that $\angle PTQ=2\angle OPQ$.
15.
A quadrilateral $ABCD$ circumscribes a circle. Prove that $AB+CD=AD+BC$.
Answer Key
Section A — Multiple Choice Questions
- (B) perpendicular
- (B) equal
- (B) $90^\circ$
- (A) $PA=PB$
- (B) right angles
Section B — Short Answer (2 marks)
- The tangent is perpendicular to the radius at the point of contact.
- $6$.
- $90^\circ$.
- They are equal ($PA=PB$).
Section C — Short Answer (3 marks)
- $120^\circ$.
- $8$.
- $70^\circ$.
- By RHS congruence of the two radius–tangent triangles, $PA=PB$.
Section D — Long Answer (5 marks)
- $\angle PTQ=2\angle OPQ$.
- $AB+CD=AD+BC$.
Generated by Vidaara.org · Assignment VID-M10-08-PRP-01 · vidaara.org