ABCD is a cyclic quadrilateral in which AB 16 5 cm BC x cm CD 11 cm AD 19 8 cm and BD is bisected by...........

Quantitative Aptitude (CGL) Geometry

ABCD is a cyclic quadrilateral in which AB = 16.5 cm, BC = x cm, CD = 11 cm, AD = 19.8 cm, and BD is bisected by AC at O. What

is the value of x ?

This questions was previously asked in

SSC CGL 4th March 2020 Shift-1

12.8 cm

12.4 cm

13.2 cm

13.8 cm

- Cyclic Quadrilateral: A quadrilateral where all vertices lie on a circle. Opposite angles sum to 180°.

- Given:

- AB = 16.5 cm, CD = 11 cm

- AD = 19.8 cm, BD is bisected by AC at O

- Hint: In a cyclic quadrilateral, intersecting chords are equal in length formulas come in handy.

- Solution:

- Use the intersecting chords theorem in the cyclic quadrilateral.

- Since AC bisects BD at O, apply Ptolemy's Theorem or properties of cyclic quadrilateral to find the relationship.

- Utilize the chord lengths replacement formula: AC × BD = AB × CD + AD × BC.

- Plug in values to solve for BC

- Answer Options:

1. 12.8 cm

2. 12.4 cm

3. 13.2 cm

4. 13.8 cm

- Final Answer: Option 3 - 13.2 cm is the correct length for BC.

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