Inscribed square between touching circles and tangent

XAT 2026 · QADI · Hard · Geometry

Consider two circles, each having radius of 5cm5\text{cm}, touching each other at a point PP. A direct tangent QRQR is drawn touching one circle at a point QQ and the other circle at a point RR. Inside the region PQRPQR inscribed by the two circles and the tangent, a square ABCDABCD is inscribed with its base ABAB on the tangent and the other side touching the two circles at points DD and CC, respectively.

Find the area of the square ABCDABCD.

  1. A.

    42 sq. cm4\sqrt{2}\text{ sq. cm}

  2. B.

    None of the other options is correct

  3. C.

    40 sq. cm40\text{ sq. cm}

  4. D.

    4 sq. cm4\text{ sq. cm}

  5. E.

    100 sq. cm100\text{ sq. cm}

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