let ABC be a right triangle in which AB=6cm,BC=8cm and angle B=900. BD is the perpendicular from B on AC. The circle through B,C,D is drawn.Construct the tangents from A to this circle.
plz sm1 explain...urgent 2mrw exam....
Consider the following situation. If a circle is drawn through the points B, D, and C, BC will be its diameter as ∠BDC is of measure 90° and BC is the hypotenuse. The centre E of this circle will be the mid-point of BC.
The required tangents can be constructed on the given circle as follows.
Join AE and bisect it. Let F be the mid-point of AE.
Taking F as centre and FE as its radius, draw a circle which will intersect the circle at point B and G. Join AG.
AB and AG are the required tangents.
The construction can be justified by proving that AG and AB are the tangents to the circle. For this, join EG.
∠AGE is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.
∴ ∠AGE = 90°
⇒ EG ⊥ AG
Since EG is the radius of the circle, AG has to be a tangent of the circle.
Already, ∠B = 90°
⇒ AB ⊥ BE
Since BE is the radius of the circle, AB has to be a tangent of the circle.