A circle is inscribed in a quadrilateral ABCD touching sides AB BC CD and AD at the points P Q R and...........

Quantitative Aptitude (CGL) Geometry

A circle is inscribed in a quadrilateral ABCD touching sides AB, BC, CD and AD at the points P, Q, R and S, respectively. If BP = 4

cm, SD = 6 cm and BC = 7 cm, then the length of DC is:

This questions was previously asked in

SSC CGL 7 June 2019 Shift-1

7 cm

8 cm

10 cm

9 cm

- A circle inscribed in a quadrilateral means that the circle touches all four sides.

- Given that the circle touches AB, BC, CD, and AD at P, Q, R, and S, respectively.

- The touching points create four segments: BP, PQ, QR, and RS.

- Key Property: The sum of segments on opposite sides of a quadrilateral with an inscribed circle is equal.

- BP = 4 cm, SD = 6 cm, BC = 7 cm.

- Let's denote the length of DC as x.

- According to the key property: BP + SD = PQ + QR and since BC and BP are part of the same side: BP + BC = SR + RD.

- Therefore, 4 + 6 = PQ + QR and BP + BC = 4 + 7 = SR + RD.

- This means PQ + QR + BC = BP + SD = 10

- So, the length of side DC is: x = 7 + 2 , giving us 9 cm.

- Answer: Option:4 - 9 cm

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