Question

a quadrilateral ABCD is draw circumscribe a circle . prove that ab+ cd = ad + bc​

Answer 1

Chapter # 10.

Class - 10.

Circles.

Answer :

Proved!

Step-by-step explanation :

Given that :

ABCD be the quadrilateral circumscribe a circle with O.

The quadrilateral touches the circle at points P, Q, R & S.

To Prove :

AB + CD = AD + BC.

Solution :

We know that :

$\bigstar\;\textbf{\underline{\underline{Lengths of the tagnets drawn from external point are Equal.}}}$

So,

$\sf \\ \\\implies AP = AS......Eq(1)\\ \\\implies BP = BQ.......Eq(2)\\ \\\implies CR = CQ.......Eq(3)\\ \\\implies DR = DS..........Eq(4)$

$\star\;\textbf{\underline{\underline{Addition of all Equations,}}}\\ \\\sf \\ \\\implies AP + BP+CR+DR = AS =BQ+CQ=DS\\ \\\implies (AP+BP) + (CR+DR)=(AS+SD) +(BQ+CQ)\\ \\\implies AB+CD = AD + BC\\ \\\bigstar\;\textbf{\underline{\underline{Hence, Proved!}}}\\ \\ \\\star\;\textbf{\underline{\underline{Refer to the Attachment for the figure.}}}$

Answer 2

Answer:

Step-by-step explanation:

• as=ap
• pb=bq
• cq=cr
• dr=ds
• tangents drawn from same point
• hence,

•     ap+pb+dr+rc=as+sd+cq+cq
• ab+cd=ad+cd
• hence proved→→