Geometry- Sample Numerical on circle in a triangle

Understand the Geometry with the help of a  Sample Numerical on circle in a triangle. Click on the link to Watch the VIDEO explanation: Watch Video

Numerical
ABC is a right - angled triangle with BC is equal to 6 cm and AB is equal to 8 cm. A circle with centre O and radius x cm is inscribed in triangle ABC. Find the value of x
Solution:
Construction: Join OF and OD 
From the fig. OD is perpendicular to AB since the radius is perpendicular to the tangent at the point of contact
OE is perpendicular to BC
OD is equal to OE since they are the radii of the same circle
Therefore ODBE is a square.
Therefore BD is equal to x and BE is equal to x
From the right - angled triangle ABC , we have AC square is equal to AB square plus BC square by Pythagoras Theorem. Enter the values of AB and BC and calculate the value of AC. Click on the Ok button to check your answer else click on the solve button to get the answer.
Therefore, Ac is equal to 10 cm
AC is equal to AF plus FC is equal to AD plus CE since the length of the tangents drawn from an external point to a circle are equal therefore AF is equal to AD and CF is equal to CE.
Therefore, AC is equal to 8 minus x plus 6 minus x this is equal to 
10 is equal to 14 minus 2 x. Calculate the value of x.
Therefore x is equal to 2 cm.

www.freewebsubmission.com