Construct a right triangle ABC with AB = 6 cm, BC = 8 cm and $∠$ B = $90^{\circ}$ . Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle. [4 MARKS]

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Solution

Construction : 3 Marks
Steps of construction : 1 Mark

Steps of construction :

1. Construct $Δ$ ABC with given measurements.

2. From B, draw $B D ⊥ A C$ .

3. Bisect BC at point O.

4. With O as centre and radius OB, draw a circle.This circle passes through B, C and D

5.The required circle is obtained.

6. Join AO and bisect it at M.

8. With M as the centre and radius equal to AM, draw a circle cutting the previous circle at the points T and B.

9. Join AT. AT and AB are the required tangents.

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