Prove that xa+ar=xb+br of circle, Mathematics

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In figure, 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

119_circle2.png

Ans:    Since the length of tangents from external point to a circle are equal

XP = XQ PA = RA BQ = BR

XP = XQ

⇒XA + PA = XB + BQ

⇒XA + AR = XB + BR (Θ PA = AR & BQ = BR)

Hence proved


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