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XAT 2015 — QA & DI Question 21

Geometric CentersEasy

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.

Answer & solution

  • A

    240000

  • 387072

  • C

    480000

  • D

    506447

  • E

    None of the above

Solution

OA ⊥ PQ, OB ⊥ PR

OP = OQ = OR = 625 cm

In ∆OAQ, OA = 175 cm and OQ = 625 cm ⇒ AQ = 600 cm

Similarly, PA = PB = RB = 600 cm

∆PQR is an isosceles triangle and PQ = PR = 1200 cm

So, PC ⊥ QR

In ∆PBO and ∆PCR,

∠OPB ≅ ∠RPC   … (Common angle)

∠PBO ≅ ∠PCR   … (Right angle)

∆PBO ~ ∆PCR       … (AA test of similarity)

∴PBPC=BOCR=POPR

∴600PC=175CR=6251200

∴ PC = 1152 cm and CR = 336 cm

∴ QR = 672 cm

A(△PQR) = 12×672×1152 = 387072

Hence, option (b).

XAT 2015 QA & DI Q21: The centre of a circle inside a triangle is at a distance of 625 cm. from each of the vertices of the triangle — Solution | TheCATExam