There are 12 uniformly spaced points on a circle with radius 10. Each of these points is joined with the two adjacent points by straight lines. Find the perimeter of the polygon so formed.
Hello sir , kindly share the solution to this problem -
hi sir, please help
Hi Richa
If we see clearly red curve is made by joining half circumference of each circle so
Req arc = 4( half circumference)
= 4* pi* 6
=24 pi
Hi Anikat,
This is what I too thought, but red curve isn't half the circumference of each circle. The answer isn't 24pie but 20pie.
Hi richa,
Sir has highlighted a equilateral triangle which will be formed between two circle.... And then at the centre of upper left circle two 60 and one 90 angle will be formed by square and equilateral traingle we can then find the remaining angle =360-(60+60+90)=150
Now for finding perimeter of any arc of circle we apply = [(angle made by arc at the centre)/360] * 2pi* r
Hope you get it now.
hi, richa
area of smaller circle =1
r=1/√pi
therefore, R=r/3
so this fig will be made
I could only come up with this solution if u get a better solution please do share in future
Hello sir , kindly solve this question -
AB and CD are two mutually perpendicular diameters of the circle shown and DF is a chord such that DE = 5 and EF = 3. Find the area of the circle.
ans: 20pie
Join C - F
∆CFD ~ ∆EOD
CD/FD = ED/OD
2r/8 = 5/r
2r² = 40
r² = 20 .
Area of the circle : πr² = 20π