10th Class Math Chapter 13 Solution Notes | Get Now
10th Class Math Chapter 13 Solution Notes cover the topic of Practical Geometry – Circles, a construction-based chapter in the matric syllabus. This chapter deals with drawing circumcircles, inscribed circles, escribed circles, regular polygons, and tangents using compass and ruler.
Credit to taleem360.
These 10th Class Math Chapter 13 Solution Notes are prepared according to the latest Punjab Board syllabus and explain every construction with clear step-by-step instructions.
For More Notes Visit Now.
What Is Covered in Chapter 13?
Chapter 13 of 10th Class Math focuses entirely on geometric constructions related to circles and triangles. The main topics include:
- Circumcircle, inscribed circle, and escribed circle of a triangle
- Bisecting a line segment and an angle
- Drawing parallel lines
- Inscribing and circumscribing squares and regular hexagons
- Constructing tangents to a circle
- Direct and transverse common tangents to two circles
Understanding these constructions step by step helps students score full marks in the practical geometry section of the board exam.
Key Definitions in 10th Class Math Chapter 13
Before attempting constructions, students must understand a few important terms used throughout the chapter.
Types of Circles Related to a Triangle
- Circumcircle: The circle that passes through all three vertices of a triangle
- Inscribed Circle (In-circle): The circle drawn inside a triangle that touches each of its sides, with radius called in-radius (r) and centre called incentre (I)
- Escribed Circle (E-circle): A circle that touches one side of the triangle externally and the other two produced sides internally
Basic Construction Techniques
- Bisecting a Line Segment: Using arcs from both endpoints to find the perpendicular bisector
- Bisecting an Angle: Using equal arcs from the vertex and their intersection point
- Drawing Parallel Lines: Using arcs of equal radius to maintain equal distance
These basic techniques are used repeatedly throughout Chapter 13, so mastering them early makes later constructions easier.
Exercise 13.1 Solution Summary
Exercise 13.1 of 10th Class Math Chapter 13 focuses on constructing triangles and drawing their circumcircle, inscribed circle, or escribed circle. Students practice:
- Constructing a triangle with given side lengths
- Drawing perpendicular bisectors of sides to find the circumcentre
- Drawing angle bisectors to find the incentre
- Drawing the required circle using the correct radius
Circumcircle vs Inscribed Circle
- Circumcircle: Found using perpendicular bisectors of the sides, which meet at the circumcentre
- Inscribed Circle: Found using angle bisectors, which meet at the incentre
A useful pattern from this exercise is that for an equilateral triangle, the altitude equals 1.5 times the radius of the inscribed circle, and 3 times the radius of the circumscribed circle.
Exercise 13.2 Solution Summary
Exercise 13.2 introduces constructions involving squares and regular hexagons inscribed in or circumscribed about a circle.
Square Constructions
- To circumscribe a square about a circle, draw two perpendicular diameters and right angles at each point where they meet the circle
- To inscribe a square in a circle, draw a diameter and its perpendicular bisector, then join the four points on the circle
Regular Hexagon Constructions
A regular hexagon can be inscribed in a circle by marking arcs equal to the radius around the circumference. This section also introduces area comparisons between inscribed and circumscribed hexagons, showing that:
Area of inscribed hexagon = ¾ × Area of circumscribed hexagon
This relationship is a common numerical question in board exams.
Exercise 13.3 Solution Summary
Exercise 13.3 deals with constructing tangents to a circle from various positions and drawing common tangents between two circles.
Types of Common Tangents
- Direct Common Tangent: Drawn when the points of contact are on the same side of the line joining the centres
- Transverse Common Tangent: Drawn when the points of contact are on opposite sides of the line joining the centres
Steps for Drawing a Tangent from an External Point
- Draw a line segment joining the centre and the external point
- Draw a semicircle using this line segment as diameter
- Mark the point where the semicircle intersects the original circle
- Join the external point to this intersection point to get the tangent
This method works because the angle in a semicircle is always 90°, which ensures the tangent line is perpendicular to the radius.
Important Constructions Table
| Construction | Key Method |
|---|---|
| Circumcircle of triangle | Perpendicular bisectors of sides |
| Inscribed circle of triangle | Angle bisectors |
| Escribed circle | Bisectors of exterior angles |
| Square in a circle | Perpendicular diameters |
| Regular hexagon | Arcs equal to radius |
| Tangent from external point | Semicircle method using 90° angle |
Memorizing this table helps students quickly recall the right method during exams.
Tips to Score Full Marks in Chapter 13
- Always use a sharp pencil and accurate compass for clean, measurable constructions
- Label all points clearly (A, B, C, O, etc.) as shown in the given steps
- Practice each construction at least twice before the exam to build speed
- Remember that circumcircle uses perpendicular bisectors while inscribed circle uses angle bisectors
- Keep construction arcs visible, as examiners check for correct method, not just the final figure
For more chapter-wise resources, check the [internal link] for 10th Class Math notes and [internal link] for Punjab Board past papers.
These 10th Class Math Chapter 13 Solution Notes are designed to help students practice constructions and prepare confidently before their exams.
Image Alt Text: 10th Class Math Chapter 13 Solution Notes – Circle Construction Steps
FAQs
Q1. What is the main topic of 10th Class Math Chapter 13?
Chapter 13 covers Practical Geometry – Circles, including construction of circumcircles, inscribed circles, escribed circles, squares, regular hexagons, and tangents. These 10th Class Math Chapter 13 Solution Notes explain each construction with clear steps.
Q2. What is the difference between circumcircle and inscribed circle?
A circumcircle passes through all three vertices of a triangle and is found using perpendicular bisectors of the sides. An inscribed circle touches all three sides from inside the triangle and is found using angle bisectors.
Q3. How do you draw a tangent to a circle from an external point?
Join the centre to the external point, draw a semicircle on this line as diameter, mark where it crosses the original circle, then join the external point to that intersection point to form the tangent line.
Q4. What is the difference between direct and transverse common tangents?
A direct common tangent touches two circles on the same side of the line joining their centres, while a transverse common tangent touches them on opposite sides, usually crossing between the two circles.
Q5. Why is Chapter 13 important for the 10th class math exam?
Chapter 13 is important because practical geometry constructions are compulsory in the board exam and carry significant marks. Accurate compass work and correct construction steps are essential for scoring full marks.
Q6. Where can I get complete 10th Class Math Chapter 13 Solution Notes?
Complete 10th Class Math Chapter 13 Solution Notes with step-by-step construction diagrams are available on TaleemWorld.com for free download and quick revision.