The chords AB and CD intersect at P. AB=17cm, PA=9 cm, PD=12 cm a) What is the length of PB? b) PC× PD = ----------- c) Find the length of PC
Answers
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a) Length of PB is 8cm.
b) PC x PD = AP x BP
c) Length of the PC is 6cm
Given:
AB = 17cm
PA = 9cm
PD = 12cm
It is given that AB and CD chords intersect at P.
To Find:
a) The length of chord PB
b) PC x PD = ?
c) Length of PC
Solution:
a) It is given that the chords AB and CD intersect at P. Therefore,
AB = AP + BP
17cm = 9cm + BP
BP = 17-9
BP = 8cm ....................................(1)
Thus, the length of PB is 8cm.
b) We already know that the chords AB and CD intersect each other. According to the property of circles, when two chords intersect each other, the measures of the segments of the chords are equal. Therefore,
PC x PD = AP x BP.................(2)
c) From (1) PC could be found easily.
PC x 12 = 9 x 8 (∵From (1) BP = 8cm)
12PC = 72
PC = 72/12
PC = 6cm
Therefore, the length of the PC is 6cm.
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