Answer

Verified

339.9k+ views

**Hint:**First we need to make the figure from the information given in the question. Then using the property of tangents that the tangents drawn from a point to a circle are equal in length, we can equate AD and AF, BD and BE, CE and CF. Then using the values of the sides given in the question with these equations, we can determine the respective lengths of the sides AD, BE and CF.

**Complete step by step solution:**

From the information given in the above question, we can draw the following figure.

Now, we know that the lengths of the tangents from a point to a circle are equal. So from the above figure, we can say that

$\begin{align}

& \Rightarrow BE=BD=x........(i) \\

& \Rightarrow CF=CE=y........(ii) \\

& \Rightarrow AF=AD=z........(iii) \\

\end{align}$

So now we can have the following figure

Now, according to the question, the sides of the triangle AC, AB and AC are $8cm$, $10cm$ and $12cm$ respectively. So from the above figure we have

$\begin{align}

& \Rightarrow y+z=8cm........(iv) \\

& \Rightarrow x+z=10cm........(v) \\

& \Rightarrow x+y=12cm........(vi) \\

\end{align}$

Subtracting (iv) from (v) we have

$\begin{align}

& \Rightarrow x+z-\left( y+z \right)=10-8 \\

& \Rightarrow x-y=2cm.........(vii) \\

\end{align}$

Adding (vi) and (vii) we get

$\begin{align}

& \Rightarrow x+y+\left( x-y \right)=12+2 \\

& \Rightarrow 2x=14 \\

& \Rightarrow x=7cm \\

\end{align}$

Putting this in (v) we get

$\begin{align}

& \Rightarrow 7+z=10 \\

& \Rightarrow z=10-7 \\

& \Rightarrow z=3cm \\

\end{align}$

Putting this in (iv) we get

$\begin{align}

& \Rightarrow y+3=8 \\

& \Rightarrow y=8-3 \\

& \Rightarrow y=5cm \\

\end{align}$

Therefore, the side AD is

$\begin{align}

& \Rightarrow AD=z \\

& \Rightarrow AD=3cm \\

\end{align}$

The side BE is

\[\begin{align}

& \Rightarrow BE=x \\

& \Rightarrow BE=7cm \\

\end{align}\]

And the side CF is

\[\begin{align}

& \Rightarrow CF=y \\

& \Rightarrow CF=5cm \\

\end{align}\]

**Hence, the sides AB, BE and CF are $3cm$, $7cm$ and $5cm$ respectively.**

**Note:**In this question, we were not given the figure corresponding to the question. So we had to assume the locations of the points D, E and F on the triangle. For simplicity, we took these adjacent to the vertices A, B, and C respectively. But if you take them opposite to the respective vertices, then AD, BE and CF will become the altitudes and you will need to use the Pythagoras theorem for calculating the lengths of the same.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE