Question

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠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.

Answer 1

Steps of construction: 

1. Draw △ABC such that AB = 6 cm; ∠B = 90° and BC – 8 cm. 

2. Drop a perpendicular BD from B on AC. 

3. Draw the circumcircle to ABCD. Let ‘E’ be its centre. 

4. Join AE and draw its perpendicular bisector \(\overleftrightarrow{XY}\) . Let it meet AE at M. 

5. Taking M as centre and MA or ME as radius draw a circle, which’ cuts the circumcircle of △BCD at P and B.

6. Join AP and extend AB, which are the required tangents.