Solution:


Given: Line PAB is a secant and Line PT is
the tangent


To Prove: PA × PB = PT^{2}


Construction: Draw chord BT and AT


Now, In ∆ PTA and ∆ BPT,


∠ PTA = ∠ PBT [Angles in alternate segment]


∠ APT = ∠ BPT [Common angle]


∴ ∆ PTA ∼ ∆ PBT










∴ PT^{2} = PA ×
PB


Hence Proved

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A secant through point P intersects the circle in points A and B. Tangent drawn through P touches the circle at point T. Prove that PA × PB = PT^2
Given: A secant through point
P intersects the circle in points A and B.
Tangent drawn through P touches the circle at
point T. Prove that PA × PB = PT^{2}
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