Question

In the adjoining fig. In a circle with centre C and chord DE ,ahe CF perpendicular to chord DE.If diameter of a circle is 20cm and DE=16cm,then CF=?GIVE REASON​

Answer 1

$\large\sf\red{⟼L=18090×722×10}$

$\begin{gathered}\\ \large\sf\red{ ⟼ L=\dfrac{1}{2}\times \dfrac{220}{7}}\end{gathered}$

$\begin{gathered}{ \large\sf\red{⟼ L=\dfrac{110}{7}}\end{gathered}$

⟼ L=15.5

Now

⟼ CF=L+r−DE

⟼ CF=15.7+10−16

⟼ CF=25.7−16

⟼CF=9.7cm

Answer 2

DC=CF

• Diameter=20cm
• Radius=20/2=10cm

We know

$\boxed{\sf L=\dfrac{\theta}{180}\times πr}$

$\\ \large\sf\longmapsto L=\dfrac{90}{180}\times \dfrac{22}{7}\times 10$

$\\ \large\sf\longmapsto L=\dfrac{1}{2}\times \dfrac{220}{7}$

$\\ \large\sf\longmapsto L=\dfrac{110}{7}$

$\\ \large\sf\longmapsto L=15.5$

Now

$\\ \large\sf\longmapsto CF=L+r-DE$

$\\ \large\sf\longmapsto CF=15.7+10-16$

$\\ \large\sf\longmapsto CF=25.7-16$

$\\ \large\sf\longmapsto CF=9.7cm$