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Question 6
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. A circle through B, C, D is drawn. Construct the tangents from A to this circle.


Solution

Steps of Construction:
Step I: ΔABC is drawn.
Step II: Perpendicular to AC is drawn to point B which intersected it at D.


Step III: With O as a center and OC as a radius, a circle is drawn. The circle through B, C, D is drawn.
Step IV: OA is joined and a circle is drawn with diameter OA which intersected the previous circle at B and E.
Step V: AE is joined.
Thus, AB and AE are the required tangents to the circle from A.
Justification:

OEA=90 (Angle in the semi-circle)
OEAE
Therefore, OE is the radius of the circle then AE has to be a tangent of the circle. 
Similarly, AB is another tangent to the circle.

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