If a right angle triangle has sides of 9cm 12cm and 15 cm if two circle inscribed in it then find the radius of small circle
Answers
Answer:
337.5cm
Step-by-step explanation:
(AB
2
+BC
2
+AC
2
)=4(AD
2
+BE
2
+CF
2
)
AB=9cm, BC=12cm, CA=15cm
AD, BE, CF are medians
⇒AD
2
+BE
2
+CF
2
=
4
3
(AB
2
+BC
2
+AC
2
)
=
4
3
[(19)
2
+(12)
2
+(15)
2
]
=
4
3
[81+144+225]
=
4
3
×450
=337.5cm.
Answer:
Given :-
In Right angle ∆ABC the two small sides are 9cm and 12cm.
To Find :-
(i) radius circle. (ii)Area of shaded region.
Solution :-
Let the center of circle be O
And the onscribed circle be PQR
Now
A square may be formed as PBRO
Let the radii be r
Tagnets of circle are equal. So,
AP = AB - PE
AP = 9 - r
Also
AP = AQ
AQ = 9 - r
RC = BC - BR
RC = 12 - x
According to the question
Length of radius = AP + CP
15 = 9 - r + 12 - r
15 = 21 - 2r
15 - 21 = -2r
-6 = -2r
-6/-2 = r
6/2 = r
3 = r
Radius is 3 cm
Finding area of shaded region
Area of triangle = 1/2 × Base × Height
Area of circle = π r²
Area of shaded region = 1/2 × Base × Height - πr²
Area = 1/2 × 9 × 12 - π × (3)²
Area = 1/2 × 9 × 12 - π × 9
Area = 6 × 9 - 9π
Area = 54 - 9π
Area = 54 - 9(3.14)
Area = 25.74 cm²
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