Question

Prove that XA + AR = XB + BR

Answer 1

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Answer 2

Answer:

given

X be an external from where two tangents, XP and XQ are drawn on the circle.

XP=XQ......(1)

as, the length of tangents drawn from common external points is always equal.

similarly,

AP=AR.....(2)

BQ=BR.....(3)

now,

XP = AX+AP..........(4)

and

XQ = BX+BQ .........(5)

from eqn(2) and (3),

XP = AX + AR

XQ = BX + BR

FROM EQN 1,

AX + AR = BX + BR

hence proved