Question

below:
Activity I : In the adjoining figure, seg DE is
a chord of a circle with centre C.
seg CF I seg DE. If diameter of the
circle is 20 cm, DE =16 cm
Fig. 3.1
find CF.
Recall and write theorems and properties which are useful to find the solution
of the above problem.
(1) The perpendicular drawn from centre to a chord bisects the
(2)
(3)
Using these properties, solve the above problem.​

Answer 1

CF = 6 cm , The perpendicular drawn from centre to a chord bisects the chord

Step-by-step explanation:

The perpendicular drawn from centre to a chord bisects the chord

=> DF = EF = DE/2 = 16/2 = 8 cm

Diameter = 20 cm

Radius = 20/2 = 10 cm

=> CD = CE = 10 cm

Applying Pythagorean theorem

CD² = CF² + DF²

=> 10² = CF² + 8²

=> CF² = 10² - 8²

=> CF² = 100 - 64

=> CF² = 36

=> CF = 6 cm

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