Construct a tangent to a circle of radius 4cm from a point which is at a distance of 6cm from its center. OR 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.

Question

Philoid · Accepted Answer

Steps of construction

1. Draw a circle of radius 4 cm.

2. Join OM’ and bisect it. Let M be mid – point of OM’.

3. Taking M as center and MO as radius draw a circle to intersect circle (0, 4) at two points P and Q.

4. Join PM’ and QM’. PM’ and QM’ are the required tangents from M’ to circle C (0, 4).

OR

Step1: Draw circle of radius 6cm with center A, mark

point C at 10 cm from the center.

Step 2: find perpendicular bisector of AC

Step3: Take this point as center and draw a circle through A and C

Step4:Mark the point where this circle intersects our circle and draw tangents through C

Length of tangents = 8cm

AE is perpendicular to CE (tangent and radius relation)

In ΔACE

AC becomes hypotenuse

AC² = CE² + AE²

10² = CE² + 6²

CE² = 100-36

CE² = 64

CE = 8cm

Construct a tangent to a circle of radius 4cm from a point which is at a distance of 6cm from its center.OR

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.

Construct a tangent to a circle of radius 4cm from a point which is at a distance of 6cm from its center.
OR