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Answers
Answer:
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1st ans:- 10 cm
2nd ans:- 4.17 cm
3rd ans:- 12 cm²
4th ans:- 24cm
Step-by-step explanation:
-> First Explanation:-
Pythagoras theorem, we know that
AC^2 = AB^2 + BC^2
= (12)^2 + (16)^2
= 144 + 256
= 400.
AC = 20
Diameter of the circle = 20cm.
Radius will be r = d/2
= 10 cm
-> Second Explanation:-
Given : - CD is diameter which meets chord AB in E
AE = BE = 4 cm , CE = 3 cm.
To find : - Radius of the circle.
Let the radius be R.
Then,
Mark a point O a the mid point of the circle and join OB. OB = OC = R .
So , OE = ( R - 3)
By pythagoras theorem,
(R - 3)² + (4)² = (R)²
=> R² - 6R + 9 + 16 = R²
=> R² - R² - 6R = - 25
=> 6R = 25
=> R = 25/6
=> R = 4.16 cm
->3rd Explanation:-
Length of on side of rectangle is 4cm.
Now diameter of circle is equal to diagonal of rectangle.
by Pythagoras theorem
the other side is 3 cm.
the area of rectangle is product of length and breadth
3×4=12
Hence, area of rectangle is 12cm²
-> 4th Explanation:-
The shortest chord must be perpendicular to AB line
Line AB also bisects the chord.
x × x = 18 × 8
x² = 144 cm
x = 12 cm
The length of shortest chord:
= 2 × 12
= 24 cm