a friendly cricket match is organized between 2 teams the money got will be given to a charitable - Maths -

Question

a friendly cricket match is organized between 2 teams the money
got will be given to a charitable hospital The field is circular
with a ring of a uniform width If O is the centre and 4 poles are
fitted at A,B,C and Din a straight line then prove that
AB=CD=1/2(AD-BC) meritnation experts plss send the ans fast coz
2morow I hve exam

Utsav · Accepted Answer

<img alt="" src=
"https://img-nm%20mnimgs%20com/img/study_content/content_ck_images/images/CONVE%20png"
style="width: 200px; height: 199px;">
Consider the question as two concentric circles with common centre
O Aline intersects these circles at points A,B,C,D
To prove AB=CD=12(AD-BC)
Construction Draw OL⊥AD

As we know that perpendicular from the centre of a circle to a
chord bisects the chordNow since BC is a chord of the smaller
circle and OL⊥BC ∴BL=LC (1)Also AD is a chord of bigger
circle and and OL⊥AD∴AL=LD (2)Subtracting (1) from
(2),we get AL-BL=LD-LC⇒AB=CD provedNow we can write
AB+BC+CD=AD ( from figure)⇒AB+CD =AD-BC⇒AB+AB = AD-BC (as
AB = CD)⇒2AB= AD-BC⇒AB=12 (AD-BC)And as
AB=CD∴AB=CD=12 (AD-BC) proved