ABCD is a cyclic quadrilateral .If $A B ∥ C D, A D = 5 c m$ , then the length of BC is :

5 c m

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6 c m

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7 c m

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8 c m

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Solution

The correct option is A $5 c m$
If ABCD is a cyclic quadrilateral

$\Rightarrow ∠ A + ∠ C = 180^{\circ}$

$\Rightarrow ∠ A + ∠ D = 180^{\circ}$

$∴ ∠ C = ∠ D$

If $B E$ is drawn perpendicular to DC then

$∠ D = ∠ E = ∠ C$

But $A B E D$ is a parallelogram

$\Rightarrow B E = A D = 5 c m$

In isosceles $△ B E C$

$∴ B E = B C = 5 c m$

Suggest Corrections

Similar questions

A B C D

A B = 5 c m, B C = 4 c m; C D = 7 c m, A D = 6 c m

B D = 5 c m

A (□ A B C D)

4 (3 + \sqrt{6}) c m^{2}

Try to draw quadrilateral ABCD of these specifications:

(i) AB = 7 cm, BC =5 cm, CD = 4 cm, ∠B = 60°, ∠C = 140°.

(ii) AB = 8 cm, BC = 6 cm, CD = 5.5 cm, DA = 3 cm, ∠B = 50°.

(iii) AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm.

Construct a quadrliateral ABCD; if:

(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and $∠$ ABC = $75^{\circ}$ .

(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and $∠ BCD = 60^{\circ}$

(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, $∠ A = 60^{\circ}$ and $∠ B = 75^{\circ}$ .

(iv) AB = 5 cm, BC = 6.5 cm, CD = 4.8 cm, $∠ B = 75^{\circ}$ and $∠ C = 120^{\circ}$

(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

(vi) AB = AD = 5 cm, BD = 7 cm and BC = DC = 5.5 cm

Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD= 7cm and BD=8cm?

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