You visited us 1 times! Enjoying our articles? Unlock Full Access!

Functions

For triangle ...

Question

For triangle $A B C$ , $R = 5 / 2$ and $r = 1$ . Let $I$ be the incenter of the triangle and $D, E$ and $F$ be the feet of the perpendiculars from $I$ to $B C$ , $C A$ and $A B$ , respectively.
The value of $\frac{I D \times I E \times I F}{I A \times I B \times I C}$ is equal to ?

\frac{5}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{5}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{10}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{1}{10}$
From the figure, $\frac{I D}{I C} = sin \frac{C}{2}$
Similarly, $\frac{I E}{I A} = sin \frac{A}{2}$
and $\frac{I F}{I B} = sin \frac{B}{2}$
Thus, $\frac{I D \times I E \times I F}{I A \times I B \times I C} = sin \frac{A}{2} sin \frac{C}{2} sin \frac{B}{2}$
$= \frac{r}{4 R} = \frac{1}{4 \times \frac{5}{2}} = \frac{1}{10}$

Suggest Corrections

Similar questions

Find the correct order for constructing an incircle for triangle $△$ ABC:

1.Draw a perpendicular from I to any side to a point D.

2.The angular bisectors intersect at the incenter I.

3.Draw the angular bisectors of $∠$ A and $∠$ B.

4.Take ID as the radius and draw a circle.

5.Construct triangle $△$ ABC.

r_{1}, r_{2}, a n d r_{3}

\frac{r_{1}}{r - r_{1}} + \frac{r_{2}}{r - r_{2}} + \frac{r_{3}}{r - r_{3}} = \frac{r_{1} r_{2} r_{3}}{(r - r_{1}) (r - r_{2}) (r - r_{3})}

A B C

I

r

D, E, F

I

B C, C A

A B

r_{1}, r_{2} r_{3}

\frac{r_{1}}{r - r_{1}}_\frac{r_{2}}{r - r_{2}} + \frac{r_{3}}{r - r_{3}} = \frac{r_{1} r_{2} r_{3}}{(r - r_{1}) (r - r_{2}) (r - r_{3})}

(\to A D + \to B E + \to C F) : \to C K

A \equiv (2, 5), B \equiv (5, 2) a n d C \equiv (- 1, - 1)

x y - x - y - 3 = 0

H \equiv (α, α)

Δ D E F

r

Join BYJU'S Learning Program