Exercise 10.2 Class 10 Math Solutions – Tangent Constructions to Circles & Arcs, Punjab Board

Solved Exercise 10.2 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering compass constructions of tangents to circles and arcs without using the centre, tangents from points on and outside the circumference, and tangents meeting at specified angles.

This page provides complete solved solutions for Exercise 10.2 from Unit 10: Practical Geometry of Circles, Class 10 Mathematics, Punjab Board (PCTB). It covers precision compass and straightedge constructions for drawing tangents to circles and arcs without using the centre (midpoint, endpoint, and external point cases), drawing tangents from points on and outside the circle, and constructing pairs of tangents meeting at a given angle. Fully labeled figures and step-by-step instructions are provided for Matric Part 2 students.
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Exercise Overview

Exercise 10.2 in Unit 10: Practical Geometry of Circles of Class 10 Punjab Board Mathematics advances students' drafting capabilities into intricate circle tangent constructions. It emphasizes the practical realization of Euclidean tangent theorems using straightedges and compasses.

The exercise systematically covers all key tangent construction scenarios: drawing a tangent to a given circular arc without utilizing the centre across three distinct conditions (point P as the midpoint of the arc, point P as an endpoint of the arc, and point P situated outside the arc); drawing tangents when the contact point lies on the circumference; constructing tangent pairs from external points using diameter-bisected auxiliary circles; and drawing two tangents that intersect each other at a prescribed angle using the supplementary central angle method.

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), tangent construction problems from Exercise 10.2 frequently appear in Section C as practical geometry long questions. Practicing these structured, step-by-step construction notes with clean geometric diagrams ensures precision and secures top marks.

FAQs

Are these Exercise 10.2 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 10 Exercise 10.2 tangent construction techniques for the 2026-2027 session.
How is a tangent drawn to a circle at a point on its circumference using the centre?
Join the centre O to the given point P on the circumference to form the radial segment OP, and construct a perpendicular line at P to OP using a compass.
How do you construct a tangent to an arc without using its centre when P is the midpoint?
Join endpoints A and B of arc AB, draw chord AB, and at midpoint P construct a line parallel to chord AB; the resulting line is the required tangent at P.
How is a tangent drawn to an arc at one of its endpoints without using the centre?
Construct an alternate segment angle on the arc and recreate an equal angle at the endpoint P with the chord to draw the tangent line.
How are two tangents drawn to a circle from an external point P?
Join OP, bisect OP at M, draw a semi-circle or auxiliary circle with centre M and radius MP intersecting the given circle at T1 and T2, and join PT1 and PT2.
How do you construct two tangents meeting each other at a given angle α?
Draw two radii of the circle inclined to each other at the supplementary angle (180° - α) at the centre, and construct perpendiculars at the endpoints of these radii; they will intersect at the required angle α.
Are clear Steps of Construction provided for all cases in Exercise 10.2?
Yes, every construction case includes detailed sequential steps, instrument settings, and fully labeled geometric diagrams.
Can students read these Exercise 10.2 solutions online?
Yes, the complete solved PDF notes for Exercise 10.2 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 10.2 solutions free for students?
Yes, all Exercise 10.2 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.