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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
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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