Question

28.
AB and CD are the diameters of the circle with centre O, AB is perpendicular to
CD, and chord DF intersects AB at E. If DE = 6 and EF = 2, then find the area of the circle.

Answer 1

Answer:

134 is the area of the circle

Answer 2

Given:

DE = 6 and EF = 2

To find:

the area of the circle.

Solution:

1) We all know that the diameter forms 90° angle at the edge of the circle.

2) So in ΔDCF(by Pythagoras theorem)

• DF²+FC²=CD²

• 8² + FC² = CD²

3) here we go by the hit and trial method.

4) We have the triplet of the 8 as (8,6,10) and (8,75,17)

5)It is clear that CF cannot be 15 as CF<DF.

6) So (8,6,10) must be the triplet  then CD = 10 cm and radius is 5 cm.

7) Area of the circle is πr² = 22/7×5×5 = 78.5 cm².

The area of the circle 78.5 cm²