Suppose that the area between a pair of concentric circles is 49pi. Find the length of a chord in the larger circle that is tangent to the smaller circle.

Answer:14 unitsStep-by-step explanation:We are given that the area between two concentric circles is [tex]49\pi[/tex]We have to find the length of chord in the larger circle that is tangent to the smaller circle.Let [tex]r_1,r_2[/tex] be the radius of two circles.[tex]r_1[/tex] be the radius of small circle and [tex]r_2[/tex] be the radius of large circleWe know that area pf circle=[tex]\pi r^2[/tex]Area of large circle =[tex]\pi r^2_2[/tex]Area of small circle =[tex]\pi r^2_1[/tex]Area between two circles =[tex]49\pi[/tex]Area of large circle -Area of small circle=[tex]49\pi[/tex][tex]\pi r^2_2-\pi r^2_1=49\pi[/tex][tex]\pi(r^2_2-r^2_1)=49[/tex]By pythagorus theorem [tex]AD^2=OA^2-OD^2[/tex][tex]AD^2=r^2_2-r^2_1[/tex][tex]AD=49[/tex][tex]AD=\sqrt{49}=7[/tex]Length of chord=[tex]2\cdot AD[/tex]Hence, the length of chord of the larger circle =[tex]2\cdot7=14[/tex] units