three congruent circles with Centre A B and C with radius 5 cm each then find the perimeter of triangle ABC and what is the length of side DE triangle DE.
Answers
Answer:
perimeter=30 cm
length of side DE=5cm
Step-by-step explanation:
length of DB=5 cm(Radius)
length of AD, AF, FC, CE, EB=5cm(Radii)
length of AB=10 cm(AD +DB)
length of AC, BC=10 cm(AF+FC and BE + EC)
perimeter of triangle ABC=AB+BC+CA=10+10+10=30cm
because length of all sides of this triangle are equal,therefore this triangle is an equilateral triangle,therefore all the angles are 60°.
therfore,angle ABC=60°
therefore angle DBE=60°
also, because DB=EB=5cm
therefore, angleBDE=angleBED(because base angles of isosceles triangles are equal)
angle BED+angleBDE+angleDBE=180°(angle sum property of triangle)
AngleBED+angleBED+60°=180°(replacing values for angleBDE and angleDBE)
2*angleBED=120°
angleBED=60°
angleBDE=60°(angleBDE=angleBED)
therefore, triangle BDE is an equilateral triangle(all angles are 60°)
therefore,BD=BE=ED(all sides of equilateral triangle are equal)
therefore, ED=5cm
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