Given: Length of each chord = 8 cm Distance between chords = 6 cm Formula: Pythagoras Theorem Hypotenuse = H, Base = B and Perpendicular = P H2=B2+P2 Calculation:
AB and CD are two chords length of each is 8 cm.O is the center of the circle and M is mid point of AB and Q is the midpoint of CD Let OB = OD = r (radius of circle) MQ = 6 cm (Given) Let OM = x, then OQ = (6 - x) cm In right angled ΔMOB OB2=OM2+MB2 ⇒r2=x2+42 ⇒x2=r2−16 ----(1) In right angled ΔQOD OD2=OQ2+QD2 ⇒r2=(6−x)2+42 ⇒r2=36+x2−12x+16 ⇒x2=r2+12x−52 ----(2) From equation (1) and equation (2) r2−16=x2=r2+12x−52 ⇒12x=36 x=3 Now, r2=x2+42 ⇒r2=32+42 ⇒r2=9+16 ⇒r=√25 ⇒r=5 ∴ Length of radius of the circle is 5 cm.