Question
Draw a right triangle ABC in which AB = 6cm, BC = 8cm and $\angle\text{B}=90^\circ.$ Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.
✓
Answer
Steps of Construction: Draw a line segment BC = 8cm. From B draw an angle of 90°. Draw an arc BA = 6cm cutting the angle at A. Join AC.$\triangle\text{ABC}$ is the required A.
Draw $\bot$ bisector of BC cutting BC at M. Take M as centre and BM as radius, draw a circle. Take A as centre and AB as radius draw an arc cutting the circle at E. Join AE. AB and AE are the required tangents. Justification:$\angle\text{ABC}=90^\circ$ (Given)
Since, OB is a radius of the circle.$\therefore$ AB is a tangent to the circle.
Also AE is a tangent to the circle.
Draw $\bot$ bisector of BC cutting BC at M. Take M as centre and BM as radius, draw a circle. Take A as centre and AB as radius draw an arc cutting the circle at E. Join AE. AB and AE are the required tangents. Justification:$\angle\text{ABC}=90^\circ$ (Given)
Since, OB is a radius of the circle.$\therefore$ AB is a tangent to the circle.
Also AE is a tangent to the circle.
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