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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-08-EXT-01
Tangents from an External Point — Assignment
Chapter: Circles
Topic: Tangents from an External Point (Geometrical Applications)
Maximum Marks: 35
Time: 75 minutes
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.
Tangents from an external point are:
  • A.equal
  • B.unequal
  • C.perpendicular
  • D.parallel
2.
The tangent length (distance $d$, radius $r$) is:
  • A.$\sqrt{d^2-r^2}$
  • B.$\sqrt{d^2+r^2}$
  • C.$d-r$
  • D.$dr$
3.
If tangent length $=8$ and radius $=6$, then $OP=$
  • A.$10$
  • B.$14$
  • C.$2$
  • D.$48$
4.
An incircle touches each side of a triangle at:
  • A.$0$ points
  • B.$1$ point
  • C.$2$ points
  • D.$3$ points
5.
The tangent length from a point on the circle is:
  • A.$r$
  • B.$0$
  • C.$2r$
  • D.$1$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the tangent length from a point $17$ cm from the centre, radius $8$ cm.
7.
If two tangents from $P$ each have length $9$, then $PA=PB=$
8.
Find the tangent length from a point at distance $25$, radius $7$.
9.
The incircle of a triangle touches each side at how many points?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
An incircle touches $BC,CA,AB$ at $D,E,F$ with $BD=4,\ CE=5,\ AF=3$. Find the sides $AB,BC,CA$.
11.
From an external point $P$, the tangent length is $24$ cm and $OP=25$ cm. Find the radius.
12.
Two tangents are drawn from $P$ to a circle of radius $3$; if $OP=5$, find the tangent length.
13.
$PA$ and $PB$ are tangents with $PA=10$ and $AB=12$. Find the perimeter of $\triangle PAB$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A circle is inscribed in $\triangle ABC$ with $AB=12,\ BC=8,\ CA=10$. Find the lengths of the tangents from $A$, $B$ and $C$.
15.
Prove that a parallelogram circumscribing a circle is a rhombus.

Answer Key

Section A — Multiple Choice Questions
  1. (A) equal
  2. (A) $\sqrt{d^2-r^2}$
  3. (A) $10$
  4. (B) $1$ point
  5. (B) $0$
Section B — Short Answer (2 marks)
  1. $15$ cm.
  2. $9$.
  3. $24$.
  4. One.
Section C — Short Answer (3 marks)
  1. $AB=7,\ BC=9,\ CA=8$.
  2. $7$ cm.
  3. $4$.
  4. $32$.
Section D — Long Answer (5 marks)
  1. From $A$: $7$; from $B$: $5$; from $C$: $3$.
  2. It is a rhombus (all sides equal).
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