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In a triangle ABC, the lengths of the sides AB and AC are 17.5cm and 9cm. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD=3cm, then what is the radius (in cm) of the circle circumscribing the triangle?
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- It is a simple formula based trigonometric one.
Given: AB = c = 17.5;AC = b = 9; Let base = BC = a; height = AD = 3;
To find: circum radius = R
Area of the triangle ABC = Δ = ½ (BC)(AD) = ½ (a)(3) = 3a/2
The formula here is : R = abc/4Δ = abc / 4(3a/2) = bc/6 = (17.5)(9)/6 = 26.25 - 11 years agoHelpfull: Yes(20) No(0)
- AS AD IS PERPENDICULAR TO BC AND AD=3CM,AS WE KNOW THAT WHEN PERPENDICULAR FROM EVERY VERTICES DROP ON OPP.SIDE OF THE TRIANGLE,THEN ALL THE PERPENDICULAR LINE MEET AT A POINT(SAY O) i.e CIRCUMCENTER AND DIVIDE EACH PERPENDICULAR LINE IN THE RATIO 2:1.IF THE LENGTH OF THE AD=3CM THEN THIS LINE GET BISECTED IN THE RATIO 2:1 BY O. AO=(2/3)*3=2CM.RADIUS=2CM
- 11 years agoHelpfull: Yes(10) No(7)
- Firstly, Calculate the base of triangle.. by using pythagoras theorem.
We get, CD as (81-9)(using Pythagoras theoerm)6*1.414(i.e. six root 2) now the length of DB is 17.24 (using square root of (17.5^2-9)
Now use formula A= abc/4R where R is the circumradius.
{1/2 x 3 x (17.24+ 6*1.41)}= {9 x 17.5 x (17.24+ 6*1.41)}/4R
Which will give the value of R as 25.75 ans. - 11 years agoHelpfull: Yes(10) No(1)
- 7.36..circum radius R=abc/(4*del)
- 11 years agoHelpfull: Yes(1) No(7)
- the radius will be 2cm
we know that the ratio is 2:1 to draw the circle circumscribing the triangle.
so 2/3*3=2 - 11 years agoHelpfull: Yes(0) No(1)
- its nearly about 18.04.find sides and simply apply circum radius formula
- 11 years agoHelpfull: Yes(0) No(0)
- nearly the radius is 25.72.
- 11 years agoHelpfull: Yes(0) No(0)
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