SATHEE: Properties of Triangles 3 Question 19

Properties of Triangles 3 Question 19

19. The exradii $r_{1}, r_{2}, r_{3}$ of $△ A B C$ are in HP, show that its sides $a, b, c$ are in AP.

$(1983, 3 M)$

Integer Answer Type Question

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Solution:

Since, $r_{1}, r_{2}$ and $r_{3}$ are exradii of $△ A B C$ are in HP.

$\begin{array}{ll} ∴ & \frac{1}{r_{1}}, \frac{1}{r_{2}}, \frac{1}{r_{3}} are in AP. \\ \Rightarrow & \frac{s - a}{Δ}, \frac{s - b}{Δ}, \frac{s - c}{Δ} are in A P . \\ \Rightarrow & s - a, s - b, s - c are in A P . \\ \Rightarrow & - a, - b, - c are in A P . \\ \Rightarrow & a, b, c are in AP. \end{array}$

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Properties of Triangles 3 Question 19

19. The exradii r1,r2,r3 of △ABC are in HP, show that its sides a,b,c are in AP.

Integer Answer Type Question

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19. The exradii $r_{1}, r_{2}, r_{3}$ of $△ A B C$ are in HP, show that its sides $a, b, c$ are in AP.