In the given figure $D A ⊥ A B, C B ⊥ A B$ and $O M ⊥ A B$ . If $A O = 5.4$ cm, $O C = 7.2$ cm and $B O = 6$ cm, then the length of $D O$ is:

4.5

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4

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5

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6.5

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Solution

The correct option is A $4.5$ cm
Since $D A, O M$ and $C B$ are perpendicular to $A B$ .
We have $D A ∥ O M ∥ C B$
Now $A C$ and $D B$ are to transversals to these parallel lines
The result of proportionals intercepts on parallel lines.
$\Rightarrow \frac{A O}{O C} = \frac{D O}{B O}$
$\Rightarrow \frac{5.4}{7.2} = \frac{D O}{6}$
$\Rightarrow \frac{5.4 \times 6}{7.2} = 4.5$ cm

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Similar questions

D A ⊥ A B, C B ⊥ A B

O M ⊥ A B

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

∆ O A B ~ ∆ O C D . If A B = 8 cm, B O = 6.4 cm, O C = 3.5 and C D = 5 cm,

In the given figure, ON = OM. If AB = 5 cm, then CD is equal to:

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