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CBSE Class 9 Answered

in a parallelogram ABCD, AB=12cm amd AD=8cm. the bisector of <A meets DC at P. AP and BC are produced to meet at Q as shown in the figure. find the lenght of CQ
Asked by sanjeev.mami | 10 Mar, 2016, 10:37: PM
answered-by-expert Expert Answer
 
begin mathsize 12px style AP space is space the space bisector space of space angle straight A. Hence comma space angle DAP equals angle PAB.... left parenthesis 1 right parenthesis Also comma space angle PAB equals angle DPA space left parenthesis opposite space internal space angles right parenthesis.... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis angle DAP equals angle DPA Hence comma space DPA space is space an space isosceles space triangle. DP equals DA equals 8 Hence comma space PC equals DC minus DP equals 12 minus 8 equals 4 space angle CPQ equals angle DPA equals straight a.... left parenthesis 3 right parenthesis angle DAP equals angle PQC equals straight a.... left parenthesis 4 right parenthesis From space left parenthesis 3 right parenthesis space and space left parenthesis 4 right parenthesis comma angle CPQ equals angle PQC Hence comma space PQC space is space an space isosceles space triangle. CQ equals PC equals 4 end style
Answered by satyajit samal | 11 Mar, 2016, 02:50: PM

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