**SUBJECT: MATHEMATICS**

**CLASS: SS 2**

**DATE:**

**TERM: 3rd TERM**

**REFERENCE BOOKS**

- New General Mathematics SSS2 by M.F. Macrae etal.
- Essential Mathematics SSS2 by A.J.S. Oluwasanmi.
- Exam Focus Mathematics.

WEEK ONE

**TOPIC: TANGENTS FROM AN EXTERNAL POINT**

**Theorem**:

**The tangents to a circle from an external point are equal.**

Given: a point T outside a circle, centre O, TA and TB are tangents to the circle at A and B.

**To prove**: |TA| = |TB|

**Construction**: Join OA, OB and OT

In âs OAT and OBT

OAT = OBT = 900 (radius tangent)

|OA| = |OB| (radii)

|OT| = |OT| (common side)

âOAT = âOBT (RHS)

|TA| = |TB|

Note that

**Example:**

1.In the figure below O is the centre of the circle and the TA and TB are tangents if

In âTAX

AXT = 900 (Symmetry)

TAX = 180 – (900 + 390) sum of angles of ()

1800 – 1290 = 510

TBX = 510 (symmetry)

OR

â ATB is an Isosceles triangle

|AT| =|BT| (tangents from external point)

< ATB = 2(39) = 780

2TBX = 1800 – 780 (sum of angle in a

2 TBX = 1020

TBX= 1020

2

TBX = 510

2.PQR are three points on a circle Centre O. The tangent at P and Q meet at T. If < PTQ = 620 calculate PRQ.

**Solution**

Join OP and OQ

In quadrilateral TQOP

POQ = 3600 – (900 + 900 + 620) sum of angle in a quadrilateral)

POQ = 3600 – 2420

POQ = 1180

PRQ = 1180 = 590 (2x angle at circumference = angle at centre)

2

PR1QR is a cyclic quadrilateral

R + R1 = 1800 (opp. angles of a cyclic quadrilateral )

R1 = 1800 – R

R1 = 1800 – 590

R1 = 1210

PRQ = 590 or 1210

**Evaluation **

- ABC are three points on a circle, centre O such that
0, the tangents at B and C meet at T. Calculate < BTC.

**GENERAL EVALUATION/REVISION QUESTIONS**

- AB is a chord and O is the centre of a circle. If AOB = 780 calculate the obtuse angle between AB and the tangent B.

1 The dimension of a cuboid metal is 24cm by 21cm by 10cm, if the cuboid is melted and used in making a cylinder whose base radius is 15cm find the height of the cylinder.

2 The volume of a cylinder is 3600cm3 and its radius is 10cm calculate its

(a) curve surface area

(b) total surface area

**READING ASSIGNMENT**

Essential Mathematics, pages149-151, numbers 11-20.

**WEEKEND ASSIGNMENT**

Use the diagram below to answer the questions.

1.If < ATO = 360 ,calculate < ABO.

(a) 360 (b) 720 (c) 180 (d) 440

2.If

3.If< BTO = 440, calculate

4.If |AB| = 18cm and |TB| = 15cm, calculate |TX|

(a) 180 (b) 330 (c) 780 (d) 120

5.If < AOT = 470, calculate ABO (a) 470 (b) 940 (c) 1330 (d) 430

**THEORY**

1.O is the centre of a circle and two tangents from a point T touch the centre at A and B. BT is produced to C. If

2.AD is a diameter of a circle,AB is a chord and AT is a tangent. a) State the size of

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