distance of a chord AB from the centre of the circle is 4cm if the length of a chord AB - Maths - Circles

Question

distance of a chord AB from the centre of the circle is 4cm if
the length of a chord AB is 6cm,then find the diameter of the
circle

Lalit Mehra · Accepted Answer

Dear Student!

Let the radius of the circle be r cm AB is the chord of the circle and O is the centre of the circle Given, AB = 6 cm, OD âŠ¥AB and OD = 4 cm OD âŠ¥ AB, $∴ AD=BD= \frac{AB}{2} = \frac{6 cm}{2} = 3 cm$ (Perpendicular from the centre of a circle to a chord bisects the chord) In right Î”ODA, OA2 = AD2 + OD2 $∴ {OA}^{2} = (3 cm)^{2} + (4 cm)^{2} = 9 {cm}^{2} + 16 {cm}^{2} = 25 {cm}^{2} \Rightarrow OA= \sqrt{25 {cm}^{2}} = 5 cm$ Radius of the circle, OA = 5 cm âˆ´ Diameter of the circle = 2 Ã— Radius of the circle = 2 Ã— 5 cm = 10 cm Cheers!

distance of a chord AB from the centre of the circle is 4cm.if the length of a chord AB is 6cm,then find the diameter of the circle