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I6. AB is a diameter of a circle. AH and BKAB.are perpendiculars from A and B respectively to the tangent at P. Provethat AH + BK |
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Answer» SOLUTION:[FIGURE IS IN THE ATTACHMENT]Given:AH and BK are perpendiculars drawn from A and B on tangent at P.To Prove:AH + BK = ABPROOF:ABKH is a rectangle.(AH & BK are Perpendiculars.AB = HK …..…….....(1)[Opposite sides of rectangle are equal]We know that, the lengths of tangents drawn from an external point to the circle are equal.AH = HP ……............(2)BK = PK ..….............(3)Adding eq. (2) and (3), AH + BK = HP + PK = HKAH + BK = AB [from eq. (1)] |
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