Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and $∠$ B = $90^{\circ}$ . BD is the perpendicular from B on AC. The circle through B, C, D is drawn. 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 and perpendicular BD from B on AC.

2. Construct a circle with BC as a diameter. This circle will pass through D.

3. Let O be the mid - point of BC. Join AO.

4. Draw a circle with AO as diameter. This circle cuts the circle drawn in step 2 at B and P.

5. Join AP. AP and AB are desired tangents drawn from A to the circle passing through B, C and D

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