Question

In as scalene triangle abc the altitudes ad and cf are dropped from the vertices abc to the sides bc and ab. The area kd triangle abc is known to be 18, the area of triangle bdf is 2 and length of segment df is 2root2. Find the radius of the circle circumscribing triangle abc

Answer 1

9/2 is the radius of the circle circumscribing ΔABC.

Step-by-step explanation:

Given that,

ΔABC = 18 cm

ΔBDF = 2cm

DF = $2\sqrt{2}$

As we know,

DF = bcosB = $2\sqrt{2}$

Now,

Area of ΔABC/Area of ΔDBF = AC^2/DF^2 = 18/2

AC/DF = $\sqrt{9}$

AC/DF = 3cm

AC = 3DF = $6\sqrt{2}$

b =  $6\sqrt{2}$

Now,

$6\sqrt{2}$ cosB =  $2\sqrt{2}$

cosB = 1/3

We know that,

b/sinB = 2R

($6\sqrt{2}$/$\frac{2\sqrt{2} }{3} }$) * 3= 2R                     (∵sinB = 1 - cos^2B = $\sqrt{1 - \frac{1}{9} }$ = $\frac{2\sqrt{2} }{3} }$)

∵ R = 9/2

Learn more: find the radius

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