Question

In rhe figure, Ab and CD are two parallel chords of a circle with centre O and radius 5 cm such that AB=8cm and CD = 6 cm if Op is perpendicular to AB and OQ is perpendicular to CD , determine the length PQ.

Answer 1

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Answer 2

Answer:

The length of PQ is 7 cm.

Step-by-step explanation:

Given information: The radius of the circle is 5 cm. AB=8 cm and CD = 6 cm. OP⊥AB, OQ⊥CD.

From the below figure it is noticed that triangle AOP and COQ are right angled triangle.

Perpendicular from the center always a chord bisector.

Use Pythagoras theorem in triangle AOP,

$AO^2=AP^2+OP^2$

$5^2=(4)^2+OP^2$

$25-16=OP^2$

$OP^2=9$

$OP=3$

The length of OP is 3 cm.

Use Pythagoras theorem in triangle COQ,

$CO^2=CQ^2+OQ^2$

$5^2=(3)^2+OQ^2$

$25-9=OQ^2$

$OQ^2=16$

$OQ=4$

The length of OP is 3 cm.

The length of PQ is

$PQ=PO+QO=3+4=7$

Therefore the length of PQ is 7 cm.