Understanding Engineering Mathematics

E. An equilateral triangle of side 30 cm circumscribes a circle. Find the radius of the
circle.
F.A circle of unit radius is inscribed in a right-angled isosceles triangle. Determine the
lengths of the sides of the triangle.

5.3.10 Cyclic quadrilaterals

➤➤

146 159

➤

Determine anglea:

a

C

B

D

A

O

120

°

5.4 Applications

1.A major problem in surveying occurs when there is an obstacle, such as a river, that

the survey line has to cross, but which we cannot easily walk round or put a tape

across. There are three common methods to solve this, relying on elementary geom-

etry – mainly similar triangles. These are illustrated in Figure 5.26(a), (b), (c).

FG

H

B

EC

A

F F

G

J

H G

B B

E E

D

D

C

C

A A

(a) (b) (c)

Figure 5.26

(a) A ranging pole is put atHon the far bank.CE, on the near bank, is

set off perpendicular toAB, which is constructed perpendicular to the

river. A pole is ranged in to a pointFonEHand a perpendicular is

dropped fromFontoABatG. Show that

GH=

CG×FG

EC−FG

(b) A lineDEis set out on the near bank and bisected atC.FCGis

now set out such thatFC=CG. With a poleHonABon the far