Question

Draw \[\Delta ABC\] such that, \[AB = 8cm\], \[BC = 6cm\] and \[\angle B = 90^\circ \]. Draw segment BD perpendicular to hypotenuse AC. Draw a circle passing through points B, D, A. show that line CB is a tangent of the circle.

Answer 1

Hint:
Here we will first draw the triangle with the given dimensions. Then we will draw the line BD perpendicular to the hypotenuse of the triangle ABC. Then we will draw the circle which is passing through the points B, D, A. A triangle is a two dimensional geometric shape that has three sides. The longest side of the right angled triangle is called hypotenuse.

Complete step by step solution:
To draw the triangle ABC, we will first draw a line segment of length 8cm and name it as AB. Then we will draw the angle B as \[90^\circ \] using the compass.
We will also draw a ray in that upward direction. Therefore, we get

Now we will mark \[BC = 6cm\] on the ray from the point B in the upward direction and then we will join the points C and A with the line segment. Therefore, we get

Now we will take a point D on the hypotenuse AC such that the line joining the points D and B is perpendicular to the hypotenuse AC. Therefore, we get

Now we have to draw a circle passing through points B, D, A.
So, to draw this circle we will find the circumcenter of the triangle BDA. Circumcenter of the triangle BDA is the point of intersection of the perpendicular bisector of the line BD and DA. So, we will draw the perpendicular bisector of the line BD and DA and name the point of its intersection as X. Therefore, we get

X is the circumcenter of the triangle BDA. Now by taking distance as AX and X as the center we will draw a circle which will passes through all the point B, D, A. therefore, we get

We can clearly see that the circle is only touching the line CB at a single point B. Hence the line CB is a tangent of the circle.

Note:
Here, to find out the circumcenter of a triangle we have to draw the bisectors of the side to get the circumcenter. In geometry, bisection is the division of something into two equal parts. Bisection is generally done with a line which is called a bisector. There are two main types of bisectors i.e. line segment bisector and angle bisector. Circumcenter of a triangle is the center of the triangle’s circumference.