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.
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.
Construction Procedure:
For the given circle, the tangent can be drawn as follows.
1. Draw a circle of 4 cm radius with centre “O”.
2. Again, take O as centre draw a circle of radius 6 cm.
3. Locate a point P on this circle
4. Join the points O and P through lines such that it becomes OP.
5. Draw the perpendicular bisector to the line OP
6. Let M be the midpoint of PO.
7. Draw a circle with M as its centre and MO as its radius
8. The circle drawn with the radius OM, intersect the given circle at the points Q and R.
9. Join PQ and PR.
10. PQ and PR are the required tangents.
It can be calculated manually as follows
In ∆PQO,
Since PQ is a tangent,
∠PQO = 90°. PO = 6cm and QO = 4 cm
Applying Pythagoras theorem in ∆PQO, we obtain
PQ^{2}+QO^{2} = PQ^{2}
PQ^{2}+(4)^{2} = (6)^{2}
PQ^{2} +16 =36
PQ^{2} = 36−16
PQ^{2} = 20
PQ = 2√5
PQ = 4.47 cm
Therefore, the tangent length PQ = 4.47
To prove this, join OQ and OR represented in dotted lines.
From the construction,
∠PQO is an angle in the semicircle.
We know that angle in a semicircle is a right angle, so it becomes,
∴ ∠PQO = 90°
Such that
⇒ OQ ⊥ PQ
Since OQ is the radius of the circle with radius 4 cm, PQ must be a tangent of the circle. Similarly, we can prove that PR is a tangent of the circle.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
3 years ago

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
3 years ago

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
3 years ago

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
3 years ago

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
3 years ago
 321 Forums
 27.3 K Topics
 53.8 K Posts
 0 Online
 12.4 K Members