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Cyclic Quadrilateral

The area of a...

Question

The area of a cyclic quadrilateral having lengths $a, b, c, d$ and the semiperimeter $s$ is given by-

\sqrt{(s - a^{2}) (s - b^{2}) (s - c^{2}) (s - d^{2})}

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\sqrt{(s - a) (s - b) (s - c) (s - d)}

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\sqrt{(s + a) (s + b) (s + c) (s + d)}

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None of the above

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Solution

The correct option is B $\sqrt{(s - a) (s - b) (s - c) (s - d)}$
Therefore, Answer is $B$

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Similar questions

A^{2} = (s - a) (s - b) (s - c) (s - d)

2 s = a + b + c + d, w h e r e a, b, c,

16

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

\frac{r_{1}}{(s - b) (s - c)} + \frac{r_{2}}{(s - c) (s - a)} + \frac{r_{3}}{(s - a) (s - b)} = \frac{3}{r}

t a n^{2} \frac{B}{2} = \frac{(s - a) (s - b)}{(s - c) (s - d)} .

A S O_{4} (a q) + B (s) \to A (s) + B S O_{4} (a q)

B S O_{4} (a q) + C (s) \to B (s) + C S O_{4} (a q)

C S O 4 (a q) + D (s) \to C (s) + D S O_{4} (a q)

D S O_{4} (a q) + B (s) \to N o r e a c t i o n

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