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
find CF.
Fig. 3.1
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
(2)
(3)
Using these properties, solve the above problem.​

Answer 1

Answer:

see tge attachment

Step-by-step explanation:

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Answer 2

The given question is in the adjoining figure, seg DE is

a chord of a circle with centre C.

seg CF I seg DE. If the diameter of the

the circle is 20 cm, DE =16 cm

find CF.

The theorems and properties which are useful to solve the given questions are

The perpendicular drawn from the centre to a chord bisects the chord

The diameter is twice that of the radius

the radius with the help of Pythagoras theorem, we can find the third unknown value

The longest chord of the circle is the diameter.

Using the above properties let's solve the problem

The perpendicular drawn from the centre to a chord bisects the chord.

DF=EF= DE ÷ 2= 16 ÷ 2= 8 cm.

It is given that the diameter is 20 cm, which means the radius is 10 cm.

CD = CE = 10 cm.

Applying Pythagoras theorem, we get

The square of the hypotenuse is equal to the sum of squares of two sides.

${cd}^{2} = {cf}^{2} + {df}^{2}$

let the unknown be x.

${10}^{2} = {x}^{2} + {8}^{2} \\ {x}^{2} = {10}^{2} - {8}^{2} \\ {x}^{2} = 100 - 64 \\ {x}^{2} = 36 \\ x = 6cm$

Therefore, the length of CF is 6 cm.

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