Question

plzzzz....help.....meee​

Answer 1

Answer:

Answer is given below...

Step-by-step explanation:

a) Perimeter of smaller circle=10π

Diameter of smaller circle is EG.

Let radius=r.

Then, 2πr=10π

⇒πd=10π

⇒EG=10 cm

∴ the length of EG is 10 cm.

b) We know that angle in a semicircle is 90°.

∵ EG is diameter of smaller circle, arc EAG along with EG forms semicircle.

So, ∠EAG=90°

∴∠EAG=90°

c) ∵ ∠EAG=90°,

we can use Pythagoras' Theorem:

EA²+AG²=EG²

⇒AG²=EG²-EA²

⇒AG²=10²-8²

⇒AG²=100-64

⇒AG²=36

⇒AG=√36

⇒AG=6 cm

∴AG=6 cm

d) From ∠EAG=90°,

we can prove that ∠EAG=∠GAF=∠FAH=∠HAE=90° using VOA and Linear Pair.

Now,

∠GAF=∠EAH=90°.....(i)

∠EFG(=∠AFG)=∠GHE(=∠AHE)....(ii)

∵ angles subtended by the same chord (EG) on points on the circle are equal

So, using AA criterion, you can say that

ΔAEH is similar to ΔAGF.

This means that ratio of the corresponding sides will be a constant,

or,

$\frac{AG}{AE}=\frac{AF}{AH}\\\\\implies \frac{6}{8}=\frac{12}{AH}\\\\\implies AH=12*\frac{8}{6}\\\\\implies AH=16\: cm$

∴ AH=16 cm

Hope it helps!

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