Question

In the given fig. XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA + AR = XB + BR.

Answer 1

GIVEN:
XP and  XQ are tangents of the circle from  with centre O and R is a point on the circle.

TO PROVE : XA  + AR = XB + BR.

PROOF:
XP = XQ    [X is an external point].......(1)
AP = AR     [A is an external point]......(2)
BQ = BR      [B is an external point]......(3)

From eq 1
XP = XQ
(XA + AP) = (XB + BQ)
XA + AR = XB + BR

[From eq 2 & 3 , AP = AR ,BQ = BR  ]

Hence proved.

HOPE THIS WILL HELP YOU...

Answer 2

I think it's helpful for you