Question

in the adjoining figure OD is perpendicular to the chord AB of a circle whose centre is O.if BC is a diameter show that CA=2OD

Answer 1

hey mate here is your answer ✌♥✌

Given....❤

in circle with centre o✔

od is perpendicular to ab❤

and BC is a diameter❣

to prove......❤

ac=2od✔

proof......❤

as od is perpendicular to ab❣

by the ppty of circle❤

ad=be....1✔

also oc=ob......radii of CIRCLE❤

so now❣

ab=2bd... from 1....3❤

and BC=2ob. . from 2......4✔

so in triangle obd and CBA❤

angle obd=angle CBA..... common angle❣

ob/ba =db/ab=1/2......from 3 and 4❤

so by SAS similarity criteria✔

triangle obd is similar to triangle CBA❤


so by cpst❣

ob/BC=od/ac❤

so od/ac=1/2✔

so ac=2od❤

hope it will be helpful to you ✔✔✔

mark me brainliest ✌✌