InterviewSolution
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InterviewSolution
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Let ABC is a right triangle in which AB = 6 cm, BC = 8 cm,angleB=90^(@).BD is the perpendicular from B on AC. The circle through B,C and D is drawn. Construct the tangents from A to this circle. |
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Answer» Solution :Given, ABC is a right triangle in which `AB=6cm, BC=8cm,angleB=90^(@)and BD` is perpendicular to AC. Steps of Construction : 1. Draw the line segments AB = 6 cm and BC= 8 cm perpendicular to each other. JoinAC, thus `DeltaABC` is the right triangle. 2. Take mid-point F of BC as CENTRE, draw a circle with radius 4 cm , passing through B,C and D. 3. Now, join AF and bisect it. Let mid-point of AF is O. 4. Take O as centre and OA as radius, FRAW a circle which intersect the given circle (which passes through B,C and D) at B and M. 5. Now, join AB and AM, which are the required tangents. Justification : Join FM and FB. Then, `angleAMF` is the angle lie in semicircle, so `""angleAMF=90^(@)` `implies""FMbotAM` Since, FM is radius of the circle. So, AM has to be tangent of the circle with centre F. Similarly, AB is also a tangent to the circle with centre F. 
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