Question

Two chords of length 10cm and 24cm are drawn in a circle of radius=13 cm .Find the distance between the chords

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Distance\:between\:chords=17\:cm}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a circle whose two chords length and radius of circle is given.

• We have to find the distance between two chords.

$\underline\bold{Given : } \\ \implies First \: chord = 10 \: cm \\ \\ \implies Second \: chord = 24 \: cm \\ \\ \implies Radius = 13 \: cm \\ \\ \underline \bold{To \: Find : } \\ \implies Distance \: between \: two \: chords = ?$

$\bold{In \: \triangle \: OMA : }\\ \\ \bold{by \: phythagoras \: theoram : } \\ \implies ({OA})^{2} = ({OM})^{2} + ({MA})^{2} \\ \\ \implies {13}^{2} = ({OM})^{2} + {12}^{2} \\ \\ \implies169 - 144 = ({OM})^{2} \\ \\ \implies OM= \sqrt{25} \\ \\ \bold{\implies OM = 5 \: cm} \\ \\ \bold{In \: \triangle \: ONC : } \\ \\ \bold{by \: phythagras \: theoram : } \\ \implies ({OC})^{2} = ( {ON})^{2} + ({NC})^{2} \\ \\ \implies {13}^{2} = ( {ON})^{2} + {5}^{2} \\ \\ \implies 169 - 25 = ({ON})^{2} \\ \\ \implies ON = \sqrt{144} \\ \\ \bold {\implies ON= 12 \: cm} \\ \\ \bold{distance \: between \: two \: chords : } \\ \implies MN = OM+ ON \\ \\ \implies MM= 5 + 12 \\ \\ \bold{\implies MN = 17 \: cm} \\ \\ \bold{\therefore distance \: between \: chords \: is \: 17 \: cm}$