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Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Circle

Olympiad workbook · IOQM · Circle

A triangle A B C with A C=20 is inscribed in a circle m . A tangent...

A triangle

A B C

with

A C=20

is inscribed in a circle

m

. A tangent

t

to

\omega

is drawn through

B

. The distance of

t

from

A

is 25 and that from

C

is 16 . If

S

denotes the area of the triangle

A B C

, find the largest integer not exceeding S/20. A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn through B . The distance of t from

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn through B . The distance of t from

Correct answer

10

Step-by-step solution

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn through B . The distance of t from

\because \quad \sin A=\frac{16}{a}=\frac{a}{2 R} \Rightarrow a^2=32 R

Similarly,

c^2=50 R

So,

a c=40 R

Now,

a b c=800 R=800\left(\frac{a b c}{4 S}\right)

\therefore \quad S=200

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