**UNIVERSITY EXAMINATIONS: 2011/2012 **

**EXAMINATION FOR THE CERTIFICATE IN BRIDGING MATHEMATICS **

**MAT 102 GEOMETRY **

**DATE: APRIL 2012 TIME: 1½ HOURS **

**INSTRUCTIONS: Answer Question One and Any other Two Questions**

**QUESTION ONE (30 MARKS) (COMPULSORY)**

e) AB and XY are two intersecting chords of a circle. They meet at R such that AR = 4cm, XR=5cm

and RY = 3cm. Calculate the length of AB. (4 Marks)

f) Draw a triangle ABC such that 0 ∠ = ABC 50 , BC = 4cm and AB = 5cm. Produce BA to P and BC to

Q. Join AC (3 Marks)

i) Draw an escribed circle touching lines BAP, AC and BCQ. (4 Marks)

ii)Measure the radius of the circle

**QUESTION TWO (15 MARKS)**

a) Given that 0 0 0 90 ≤ ≤ θ , solve the equation 2 2 4cos 4cos 1 sin θ − += θ θ (5 Marks)

b) The length of the sides of an inscribed triangle are 10cm, 7cm and 5cm respectively. Calculate

i) The sizes of the angles of the triangle (8 Marks)

ii)The radius of the circle (2 Marks)

**QUESTION THREE (15 MARKS)**

A point A lies on the latitude 500

N and longitude 100

W, B lies on latitude 500

N and 850

W and C lies on

350

S and 100

W. Calculate

i) The distance between A and C along a great circle (3 Marks)

ii) The radius of the parallel of latitude 500

N (3 Marks)

iii)The distance between A and B along a parallel of latitude (3 Marks)

iv)The distance of B from the equator (3 Marks)

v) The length of the chord AB (3 Marks)

**QUESTION FOUR (15 MARKS)**

b) At a point A, Richard records the angle of elevation of the top (T) of the building as 220. He moves

further from the building by 28m to point B and notes that the angle of elevation of the top then is180

. Determine

i) The height of the building (5 Marks)

ii)How far he is from the bottom of the building when the angle of elevation of the top T is 100

(5 Marks)

**QUESTION FIVE (15 MARKS)**

In a quadrilateral OACB, OA = a and OB = b. OA is parallel to BC. OA=3BC and M is a point on AB

such that AM:MB = 3:1.

i) Evaluate the vectors AB, BM, OM and MC in terms of a and b (12 Marks)

ii)Show that O, M and C are collinear.