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CBSE Class 9 Answered

TWO EQUAL CHORDS AB AND CD OF A CIRCLE WHEN PRODUCED INTERSECT AT A POINT P.PROVE THAT PB=PD.
Asked by vrishti TOKAS | 22 Feb, 2016, 08:09: PM
answered-by-expert Expert Answer
 
Let space straight O space be space the space centre space of space the space circle space containing space two space equal space chords space AB space and space CD space intersecting space at space point space straight P. Join space OP. Draw space OM space perpendicular AB space and space ON space perpendicular CD. We space know space that space equal space chords space are space equidistant space from space the space centre space of space the space circle. therefore OM space equals space ON..... left parenthesis 1 right parenthesis straight A space perpendicular space drawn space from space the space centre space of space the space circle space bisects space the space chord. OM space perpendicular AB space and space ON space perpendicular CD. therefore AM space equals MB space and space CN space equals space ND therefore AB space equals space 2 MB space space and space CD space equals space 2 ND But space AB space equals space CD space space left parenthesis given right parenthesis therefore 2 MB space equals 2 ND MB space equals space ND space.............. left parenthesis 2 right parenthesis In space increment OMP space and space increment ONP OM space equals space ON space space........ left square bracket from space left parenthesis 1 right parenthesis right square bracket angle OMP space equals angle ONP....... left square bracket both space are space 90 degree right square bracket OP space equals OP space left square bracket common right square bracket therefore increment OMP space approximately equal to space increment ONP space left parenthesis By space RHS space congruence space criterian right parenthesis So space we space can space write comma space MP space equals space NP MB space plus space BP space equals space ND plus DP space ND space plus BP space equals space ND space plus space DP....... left square bracket from space left parenthesis 2 right parenthesis right square bracket therefore BP space equals space DP
Answered by Vijaykumar Wani | 23 Feb, 2016, 11:41: AM

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