#### Question

Construct a right triangle ABC with AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle.

#### Solution

Steps of construction:

1) Construct the triangle as per given measurements.

2) Take any arbitrary radius and draw two arcs of circle from point B on AC, intersecting AC at X and Y.

3) Taking X and Y as centres, draw two arcs of circles to intersect each other at point E. Join B and E. BE is the perpendicular from B on AC.

4) DBDC is a right angled. Hence, BC the hypotenuse will form the diameter of the circle passing through the vertices of ΔBDC.

5) BC = 8 cm OC = 4 cm. draw a circle of radius equal 4 cm, passing through B, D and C.

6) Join O and A. Obtain the mid-point P of segment OA by drawing perpendicular bisector to OA.

7) Draw a circle with centre P and radius AP.

8) Let B and F be the points of intersection of these two circles. Hence, AB and AF are the required tangents.