Question

draw circle of radius 6 CM take a point outside it draw a pair of tangent to the circle from P without using its centre

Answer 1

A pair of tangents to the given circle can be constructed as follows.

Step 1

Taking any point O of the given plane as centre, draw a circle of 6 cm radius. Locate a point P, 10 cm away from O. Join OP.

Step 2

Bisect OP. Let M be the mid-point of PO.

Step 3

Taking M as centre and MO as radius, draw a circle.

Step 4

Let this circle intersect the previous circle at point Q and R.

Step 5

Join PQ and PR. PQ and PR are the required tangents.

The lengths of tangents PQ and PR are 8 cm each.

Justification

The construction can be justified by proving that PQ and PR are the tangents to the circle (whose centre is O and radius is 6 cm). For this, join OQ and OR.

∠PQO is an angle in the semi-circle. We know that angle in a semi-circle is a right angle.

∴ ∠PQO = 90°

⇒ OQ ⊥ PQ

Since OQ is the radius of the circle, PQ has to be a tangent of the circle. Similarly, PR is a tangent of the circle

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Answer 2

Answer:

Step-by-step explanation:

1) First draw a circle of radius 6 cm

2)Take a point P on circle and then from that point draw a chord.

3) Draw another chord from the next point. Join all the points which form a triangle.

4) Draw an arc with appropriate radius in the second point inside the triangle and with that same radius draw another arc in P.

5)While drawing in arc P make sure it cut the triangle

6) Take the measure between the arc drawn of the second point and keep it in the point where it cut the triangle

7) Join the point of intersection of arc yo the point P

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