Question

the sum of the parameters of two squares is 76 and the difference between their areas is 57. (a) if the length of the side of the square is 76 and difference between their areas is 57. (b) what is the difference between the perimeter of the square? (c) (X+y)(X+y) =____________ (d) what are the length of the side of the square? ​

Answer 1

AP is the tangent to the circle.

∴ OA ⊥ AP (Radius is perpendicular to the tangent at the point of contact)

⇒ ∠OAP = 90º

In Δ OAP,

sin ∠OPA = OA/OP = r/2r [Diameter of the circle]

∴ sin ∠OPA = 1/2 = sin 30º

⇒ ∠OPA = 30º

Similarly, it can he prayed that ∠OPB = 30

How, LAPB = LOPP + LOPB = 30° + 30° = 60°

In APPB,

PA = PB [lengths &tangents drawn from an external point to circle are equal]

⇒ ∠PAB = ∠PBA --- (1) [Equal sides have equal angles apposite to them]

∠PAB + ∠PBA + ∠APB = 180° [Angle sum property]

∠PAB + ∠PBA + ∠APB = 180° - 60° [Using (1)]

⇒ 2∠PAB = 120°

⇒ ∠PAB = 60°

From (1) and (2)

∠PAB = ∠PBA = ∠APB = 60°

APPB is an equilateral triangle.

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