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Example 1

Two chords seg AB and seg. CD intersect in the circle at P. Given that l (seg.PC) = l (seg.PB) = 1.5 cm and l (seg.PD) = 3 cm. Find l (seg.AP).

Solution:

l (seg AP) ´ l (seg PB) = l (seg DP) ´ l (seg PC)

l (seg AP) ´ 1.5 = 3 ´ 1.5

l (seg AP) = 3 cm.

Example 2

Seg.PA and seg.PC are two secants where l (seg.PB) = 3.5 cm, l (seg.PD) = 4 cm and l (seg.DC) = 3 cm. Find l (seg.AB).

Solution:

l (seg AP) ´ l (seg BP) = l (seg CP) ´ l (seg DP)

x ´ 3.5 = 7 ´ 4

x = 8

l (seg AB) = l (seg AP) - l (seg BP)

= 8 - 3.5

= 4.5 cm.

Example 3

PT is a tangent intersecting the secant through AB at P. Given l (seg. PA) = 2.5 cm. and l (seg.AB) = 4.5 cm., find l (seg PT).

Solution:

l (seg PT)2 = l (seg PA) ´ l (seg PB)

= 2.5 ´ 7

= 17.5

l (seg. PT) = 4.2 cm.

Index

7.1 Introduction
7.2 Lines of circle
7.3 Arcs
7.4 Inscribed angels
7.5 Some properties od tangents, secants and chords
7.6 Chords and their arcs
7.7 Segments of chords secants and tangents
7.8 Lengths of arcs and area of sectors

Chapter 8

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