Question

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.

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)

∴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.

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.

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