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  • Let ABC be a right triangle in which AB equals 6 cm, BC equals 8 cm and angle B equals 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.

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

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Steps of construction:- 

(i) Draw a line segment BC of length 8 cm.

(ii) Construct a right angle at point B. Now draw a line of length 6 cm. Name the other point as A.

(iii) Join AC. \DeltaABC is the required triangle.

(iv) Now construct a line BD on the line segment AC such that BD is perpendicular to AC.

(v) Now draw a circle taking E as a centre (E is the midpoint of line BC) and BE as the radius.

(vi) Join AE. And draw a perpendicular bisector of this line.

(vii) Name the midpoint of AE as F. 

(viii) Now, draw a circle with F as the centre and AF as the radius.

(ix) Name the intersection point of both the circles as G.

(x) Join AG. Thus AB and AG are the required tangents.

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Devendra Khairwa

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