Mathematics

Mathematics

Problem

A circle with centre

O

has radius

20\,\text{cm}

. Two chords

AB

and

AC

are drawn such that

AB = 24\,\text{cm}

and

AC = 32\,\text{cm}

. Let

D

and

E

be the feet of the perpendiculars dropped from

O

to

AB

and

AC

respectively. a. (i) Show that

AD = DB

and

AE = EC

. b. (ii) Calculate

OD

and

OE

. c. (iii) Find the length of

DE

.

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