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.
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