Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

8.   A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

       Circles EXERCISE 10.2

Answers (1)

best_answer


To prove- AB + CD = AD + BC
Proof-
We have,
Since the length of the tangents drawn from an external point to a circle are equal 
AP =AS .......(i)
BP = BQ.........(ii)
AS = AP...........(iii)
CR = CQ ...........(iv)

By adding all the equations, we get;

    AP + BP +RD+ CR = AS +DS +BQ +CQ
\Rightarrow(AP + BP) + (RD + CR) = (AS+DS)+(BQ + CQ)
\RightarrowAB + CD  = AD + BC

hence proved.

Posted by

manish

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Exam 2025: Class 10, 12 practical exam dates out at cbse.gov.in; passing marks
anam-khan

CBSE urges schools to complete 100% registration of Class 9, 11 students by October 16; late fee for delays

Latest Question