Circles ncert solutions Chapter 10 Exercise 10.2 Question 8
8. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
Solution:
ABCD is a quadrilateral. All the sides of quadrilateral are tangents to the circle.
Therefore, DC, CB, AB and AD are tangents to the circle.
CR = CQ {Two Tangents drawn from an external point to the circle are equal} (1)
AP=AS {Two Tangents drawn from an external point to the circle are equal} (2)
PB=BQ {Two Tangents drawn from an external point to the circle are equal} (3)
DR = DS {Two Tangents drawn from an external point to the circle are equal} (4)
Adding (1), (2), (3), and (4), we get
Hence Proved
Exalibur says
There is no equation 5. So 5 should be removed from the adding-line (third from last). Thanks
Jashan says
thanks for letting me know. I fixed that error.