In the Fig given above, l is a line intersecting two concentric circles at points A,C,D and B - Maths - Circles

Question

In
the Fig given above, l is a line intersecting two concentric
circles at points A,C,D and B Prove that AC=DB

Priyanka Kedia · Accepted Answer

Dear Student,
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_564724054a3b1%20png"
style="width: 220px; height: 187px;">

Draw a perpendicular OP on line CD
It can be observed that CD is the chord of the smaller circle and AB is the chord of the bigger circle
We know that perpendicular drawn from the centre of the circle bisects the chord
So, PC=PD        
1And,AP=PB       
2Subtracting equation2 from 1, we get,AP-PC=PB-PD⇒AC=DBHence Proved

Hope this would have clear your doubt Do let us know in case of any
further concerns

In the Fig. given above, l is a line intersecting two concentric circles at points A,C,D and B. Prove that AC=DB