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Abc is a Triangle with Ab = 10 Cm, Bc = 8 Cm and Ac = 6 Cm (Not Drawn to Scale). Three Circle Are Drawn Touching Each Other with the Vertices as Their Centres. Find the Radii of the Three Circles - ICSE Class 10 - Mathematics

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ConceptChord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line

Question

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circle are drawn touching each other with the vertices as their centres. Find the radii of the three circles

Solution

E
Given: ABC is a triangle with AB = 10 cm, BC= 8 cm, AC = 6 cm. Three circles are drawn with centre A, B and C touch each other at P, Q and R respectively.
We need to find the radii of the three circles.
Let
PA = AQ = x
QC = CR = y
RB = BP = z
∴ x + z = 10 ….. (1)
z + y = 8 ……..(2)
y + x = 6 …….(3)
Adding all the three equations, we have
2 (x + y + z) = 24
 ⇒ x + y + =` 24/2 = 12 `       ………. (4)
Subtracting (1) (2) and (3) from (4)
y = 12 – 10 = 2
x = 12 – 8 = 4                                                            
z = 12 – 6 = 6
Therefore, radii are 2 cm, 4 cm and 6 cm

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Solution Abc is a Triangle with Ab = 10 Cm, Bc = 8 Cm and Ac = 6 Cm (Not Drawn to Scale). Three Circle Are Drawn Touching Each Other with the Vertices as Their Centres. Find the Radii of the Three Circles Concept: Chord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line.
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