Xavier Aptitude Test 2015 Paper

Question : 72 of 113

Marks: +1, -0

The centre of a circle inside a triangle is at a distance of 625 cm. from each of the vertices of the triangle. If the diameter of the circle is 350 cm. and the circle is touching only two sides of the triangle, find the area of the triangle.

240000
387072
480000
506447
None of the above

Validate

Solution:

(b)

In this figure,

{OA}=\ {OC}=\ {OE}=625 ;

then

\∠{OAD}=\∠{OCD}

Both

\ {AE}

and

\ {AC}

are tangents to the circle (with centre

{O} ) →{O}

is a point on

{AB} .

Diameter of the circle

=350 .

Then,

\ {OD}=175

Now AD

=600(

AOD is a right angle triangle)
Then,

\sin∠{OAD}=\ {\ {OD}}/{\ {AO}}=\ {175}/{625}

and

\cos ∠{OAD}=\ {\ {AD}}/{ {AO}}=\ {600}/{625}

Then, Cos ∠ACB = Cos (90° - ∠OAD)

=\sin ∠{OAD} \⇒{ {BC}}/{\ {AC}}=\ { {OD}}/{\ {OA}}

\⇒ {\ {BC}}/{1200}= {175}/{625} \⇒ \ {BC}=7×48

Again

\sin∠ {ACB}=\sin \ (90^{\°}-\∠ {OAD}\ )

=\cos ∠\ {O} \ {AD} ) \⇒{ {AB}}/{ {AC}}=\ {\ {AD}}/{\ {OA}}

\⇒{ {AB}}/{1200}=\ {600}/{625} \⇒{AB}=24 \× 48

Now, area of the triangle

{ACE}=1 / 2 ×{AB}×{EC}

=24 \× 48 \× 7× 48=387072 \ {m}^{2}

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