# Lesson Notes By Weeks and Term - Senior Secondary 1

Tangency

TERM – 2ND TERM

WEEK TEN

Class: Senior Secondary School 1

Age: 15 years

Duration: 40 minutes of 5 periods each

Date:

Subject: Technical Drawing

Topic: TANGENCY

SPECIFIC OBJECTIVES: At the end of the lesson, pupils should be able to

I.) Define tangency

II.) Discuss the principles of tangency

III.) Construct a tangent to a circle at a given point on the circumference.

IV.) Construct a common tangent between two unequal circles.

INSTRUCTIONAL TECHNIQUES: Identification, explanation, questions and answers, demonstration, videos from source

INSTRUCTIONAL MATERIALS: Videos, loud speaker, textbook, pictures,

INSTRUCTIONAL PROCEDURES

PERIOD 1-2

 PRESENTATION TEACHER’S ACTIVITY STUDENT’S ACTIVITY STEP 1 INTRODUCTION The teacher explains the meaning of tangency. Students listens attentively to the teacher STEP 2 EXPLANATION Teacher guide students to construct various tangent to circle.. Students exhibit attentiveness and active engagement STEP 3 NOTE TAKING The teacher writes a summarized note on the board The students copy the note in their books

NOTE

TANGENCY

Tangency refers to the condition where a line or curve just touches another line, curve, or surface at a single point without intersecting it. This concept is fundamental in various fields and has several principles and applications.

Point of tangency

The point of tangency is the unique point at which a given tangent line meets a geometric figure, such as a circle or plane curve. At the point of tangency, the tangent line osculates the curve but does not cross it, i.e., intersect it.

Principles:

1. Contact at a Single Point: Tangency involves the contact of two elements at a single point without crossing or intersecting. This point of contact is called the point of tangency.
2. Perpendicularity: At the point of tangency, the tangent line or curve is perpendicular to the line, curve, or surface it touches. This principle ensures smooth transitions and avoids abrupt changes in direction.
3. Smooth Continuity: Tangency promotes smoothness and continuity in technical drawings, ensuring that curves flow seamlessly into one another and maintaining aesthetic appeal.

Applications:

1. Tangency is extensively used in geometric constructions and design to create smooth transitions between different elements such as curves, lines, and surfaces.

2.In mechanical engineering, tangency is crucial for designing components with moving parts, such as gears, cams, and rollers.

1. In drafting and computer-aided design (CAD), tangency is a fundamental concept used to define relationships between different geometric entities.
2. Tangency is applied in civil engineering and surveying for designing roads, railways, and other infrastructure projects.

How to construct a tangent to a circle at a given point on the circumference

To construct a tangent to a circle at a given point on the circumference, follow these steps:

1. Draw the circle with its center and the given point on the circumference.
2. From the center of the circle O, draw a radius to the given point P and with same radius extend the line to point A.
3. Using point A with the previous radius, draw an arc above and below P, label BC
4. Join BC through point P. BC is the required tangent.

How to construct a common tangent between two unequal circles

To construct a common tangent between two unequal circles, follow these steps:

1. Draw the two circles with their centers and radii. Make sure they do not intersect.
2. Draw a line through the centers of the circles. This line will pass through the points where the common tangents touch the circles.
3. Extend the line beyond the circles.
4. Bisect the distance between the centers of the circles. This will be the midpoint of the common tangent.
5. From the midpoint, draw a perpendicular line to the line connecting the centers of the circles.
6. Where this perpendicular line intersects the line connecting the centers, draw a line parallel to the original line. This line will be one of the common tangents.
7. Repeat steps 4-6 for the other side of the circles to construct the second common tangent.

EVALUATION: 1. What is tangency

2i. Construct an internal tangent to two unequal circles of diameter 30 and 58 respectively, whose centres are 100 apart.

ii. Measure and state the distance between the points of tangency.(WAEC)

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively