Drawing Tangents to a Circle from a Point outside the Circle
Let ABC be a ...
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.
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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) ∴OE⊥AE 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.