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# Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths

**Solution:**

**Steps of construction:**

- Take a point O as the centre and 6 cm radius. Draw a circle.
- Take a point P in such a manner that OP = 10cm
- With O and P as centres and radius more than half of OP draw arcs above and below OP to intersect at X and Y.
- Draw line segment XY to intersect OP at M.
- With M as the centre and OM as radius draw a circle to intersect the given circle at Q and R.
- Join PQ and PR. PQ and PR are the tangents, where PQ and PR = 8cm.

Proof:

Since PQ ⊥ OQ (Angle in a semicircle)

∠PQO = 90º

In right ΔPQO,

OP = 10 cm, OQ = 6cm (radius)

PQ² = OP² - OQ²

= (10)² - (6)²

= 100 - 36

= 64

PQ = √64

= 8 cm

Similarly, we can prove that PR = 8 cm.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 11

**Video Solution:**

## Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths

NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 Question 1

**Summary:**

A circle of radius 6 cm is drawn. PQ and PR are the required tangents of 8 cm length each constructed from a point 10 cm away from the centre of the circle.

**☛ Related Questions:**

- Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
- Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
- Draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60°.
- Draw a line segment AB of length 8 cm. Taking A as the centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct a tangent to each circle from the centre of the other circle.

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