The square ABCD is inscribed in a circle of radius 1 unit.ABP is a straight line,PC is the tangent to the circle. The length of PD is
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The length of PD is √10 unit if The square ABCD is inscribed in a circle of radius 1 unit. ABP is a straight line,PC is the tangent to the circle.
Step-by-step explanation:
The square ABCD is inscribed in a circle of radius 1 unit
=> Diameter = 2* Radius = 2 * 1 = 2 unit
Diameter = Diagonal of square ABCD
Diagonal² = Side² + Side²
=> 2² = 2 *Side²
=> Side = √2
AB = BC = CD = AD = √2
now in Δ ABC & Δ PBC
BC = BC (common)
∠ABC = ∠PBC = 90°
∠ACB = ∠PCB = 45°
=> Δ ABC ≅ Δ PBC
=> PB = AB = √2 unit
AP = AB + BP = 2√2 unit
AD = √2 unit
PD² = AP² + AD²
=> PD² = 8 + 2
=> PD² = 10
=> PD = √10 unit
The length of PD is √10 unit
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