Question

In the given kite figure ABCD,side AD =5cm,AO=4cm. Find the length of OD and AN. Find the measure of angle AOB​

Answer 1

Answer:

Angle AOB = 90°

AO^2 + OD^2 = AD^2 [PYTHAGORAS THEOROM]

SO, 4^2 + OD^2 = 5^2

OD = root of 25 - 16 = root of 9 = 3

And OD = OB as in a kite longer diagonal bisects the shorter one.

So, OD = OB = 3 cm

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Answer 2

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Given:-

$\tt C \: bisects \; the \; kite, \therefore$

$\tt \overline{AD} = 5cm$

$\tt \overline{AO} =4cm$

$\tt \Delta AOD = \Delta AOB$

To find:-

• the measure of OD and AB
• the measure of $\tt \angle AOB$

Solution:-

1.)$\tt Measure \; of \; OD.$

$\tt \Delta AOD \ \ is \ a \ right \ \ angled \ \ triangle.$

$\tt \therefore \underline\orange{Using \: Pythagoras \: Theorem} :-$

$\implies \tt {AO}^{2}+{AD}^{2}={OD}^{2}$

$\implies \tt {4}^{2}+{OD}^{2}= {5}^{2}$

$\implies \tt {5}^{2}-{4}^{2}={OD}^{2}$

$\implies \tt 25-16 = {OD}^{2}$

$\implies \tt {OD}^{2}=9$

$\implies \tt OD= \sqrt{9}$

$\implies \tt OD=3cm$

2.) $\tt Measure \; of \; \overline{AB}$

$\implies\tt AD=AB$

$\implies\tt 5cm=AB$

3.) $\tt Measure \: of \: \Delta AOB$

$\tt \implies Since \: \Delta AOB \ is \ a \ right \ angled \ triangle,$

$\tt \therefore \Delta AOB={90}^{\circ}$

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