Question

in the figure given alongside.A tangent PT and a line segment PBA is drawn to a circle with center o.if OL . AB prove that pA× PB=PT²​

Answer 1

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in the figure given alongside.A tangent PT and a line segment PBA is drawn to a circle with center o.if OL . AB prove that pA× PB=PT²

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Given:

PT is a tangent drawn from an external point P and a line segment PAB is drawn to a circle with Centre O.ON is perpendicular on the chord AB.

ON ⟂ AB

TO PROVE:

(i) PA.PB = PN² –  AN²

(ii) PN² – AN² = OP² – PT²

(iii) PA.PB = PT².

CONSTRUCTION: In the given figure join OA.

PROOF IS IN THE ATTACHMENT

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