Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

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

Practice Circle on Quantrex Academy →

More from Circle

Let A B C D be a convex cyclic quadrilateral. Suppose P is a point in the plane of the… Olympiad workbook Let Ω_1 be a circle with centre O and let AB be diameter of Ω_1 . Let P be a point on the… Olympiad workbook A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn… Olympiad workbook A light source at the point (0,16) in the coordinate plane casts light in all directions.… Olympiad workbook Let A B be a diameter of a circle ω and let C be a point on ω , different from A and B .… Olympiad workbook Consider an isosceles triangle A B C with sides B C=30, C A=A B=20 . Let D be the foot of… Olympiad workbook A semicircular paper is folded along a chord such that the folded circular arc is tangent… Olympiad workbook Let A B be a diameter of a circle and let C be a point on the segment A B such that A C… Olympiad workbook Full Circle list All Olympiad workbook PYQs