Draw ∆ ABC such that, AB = 8 cm, BC = 6 cm and∠B = 90°. Draw seg BD
perpendicular to hypotenuse AC. Draw a circle passing through points
B, D, A. Show that line CB is a tangent of the circle.
Answers
Solution:
Steps of Construction
1. Draw a line segment AB of Length 8 cm.
2. Draw angle B= 90°,with the help of compass.Produce Ray BM in upward Direction.
3. Mark BC= 6 cm on the ray BM.
4. Join AC.
In Right Triangle ABC
AB² + BC²= AC²
8² + 6²= AC²
64 + 36= AC²
100 = AC²
AC= √100
AC= 10 cm
Choose a point D on line segment AC such that ,∠ADB=∠ADC=90°, DC=x cm, and AD=(10 -x) cm.Take B D= y cm, AB = 8 cm, BC= 6 cm.
In Δ A DB and Δ B D C
AB²= B D² + AD² ∧ BC² = B D² + DC²
8²= y² + (10 -x)² ∧ 6²= x² + y²
64 - (10-x)²= y²---(1) ∧ 36 - x²= y²------(2)
From 1 and 2,we get
64 - (10-x)²=36 - x²
64 - 36-100 - x²+20 x+ x²=0
20 x= 72
x= 3.6 cm
So, DC= 3.6 cm, and AD= 10-3.6= 6.4 cm
So, Mark, AD= 6.4 cm, On point D with the help of compass make an angle of 90° which will pass through B.
To Draw a circle passing through points B, D, A that is Circumcircle . You can draw by taking any two line segments BD and DA and drawing its perpendicular bisector. The perpendicular bisector can be drawn by opening the compass more than half of that line segment and marking arc on both sides from both the ends of line segment.
The point where the two bisectors of sides BD and DA meet is Circumcenter of triangle BAD.
Marking J as center and Either JA, JB or JD as radius draw the Circumcircle passing through vertices B, D and A of triangle B DA .
Answer:
the answer shown above me is the correct answer