Question

solve it. Challenge​

Answer 1

Step-by-step explanation:

we know one theorem that if you draw a line perpendicularly from the centre to a chord then that line divides that chord into two equal parts

so in the the point of intersection of PQ and AB take it as X

so according to the above theorem

XC= XD( for smaller circle)

XA= XB( for bigger circle)

so the value of ACDB= 2√15

so AX = 2√15/2= √15

now O'A =4 (radius of bigger circle)

so by Pythagoras theorem for the right triangle O'XA

O'A^2= O'X^2+XA^2

16= O'X^2+15

O'X^2=16-15=1

O'X= 1

and the distance between XO = 1+(4-3)=1+1=2

OA^2= OX^2+XA^2

= 4+15

OA = √19

we need to find the value of XC in order to find the value of AC

so in the triangle XOC

OC=3(radius )

XO=2

so XC^2= 3^2-2^2= 9-4=5

XC= √5

so now AC= AX-XC =√15-√5= √5(√3-1)