Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and \(\angle B=90° \) ;. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Steps to construct the required figure by the given data:
Step 1: Draw a \(\triangle \) ABC, in which AB=6cm, BC=8cm and \(\angle B=90° \) ;

Step 2: Draw BD perpen AC and also draw the perpendicular bisectors of BC and BD.They meet at point O’.

Step 3:Taking O’ as the center, draw a circle of radius O’B. This circle passes through B,C and D.

Step 4:Join O’A and draw a perpendicular bisector of O’A. This bisector meets O’A at K.

Step 5:Taking K as centre, draw an arc of radius KO’ intersects the previous circle C’ at T.

Step 6:Join AP and AQ and thus we got our required tangents.