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

Question

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and &ang; B = 90&deg;. BD is theperpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Philoid · Accepted Answer

Steps of construction:

i. Draw a line segment AB = 6 cm.

ii. Draw a right angle at point B and then, BC = 8 cm.

iii. Now, draw a perpendicular BD to AC.

iv. We know: In a right triangle, hypotenuse is the diameter of circum circle

v. Considering BC as diameter, draw a circle passing through points B, C and D.

vi. Join A to O and taking AO as diameter, draw second circle.

vii. From point A, draw tangents AB and AP.

The final figure is obtained as shown below: