Advertisements
Advertisements
Question
Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.
Solution
In order to draw the pair of tangents, we follow the following steps:
Steps of construction:
- Take a point O on the plane of the paper and draw a circle of radius OA = 4 cm.
- Produce OA to B such that OA = AB = 4 cm.
- Taking A as the centre draw a circle of radius AO = AB = 4 cm. Suppose it cuts the circle drawn in step 1 at P and Q.
- Join BP and BQ to get desired tangents.
Justification:
In ∆OAP, we have
OA = OP = 4 cm ...(∵ Radius)
Also, AP = 4 cm ...(∵ Radius of circle with centre A)
∴ ∆OAP is equilateral
⇒ ∠PAO = 60°
⇒ ∠BAP = 120°
In ∆BAP, we have
BA = AP and ∠BAP = 120°
∴ ∠ABP = ∠APB = 30°
⇒ ∠PBQ = 60°
APPEARS IN
RELATED QUESTIONS
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.
Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.
Draw a circle circumscribing a regular hexagon with side 5 cm.
Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.
Draw a circle of radius 4.2. Draw a pair of tangents to this circle inclined to each other at an angle of 45°
A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of width of 0·7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq. m ?
Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Draw two circles of radii 3.5 cm and 2 cm respectively so that their centres are 6 cm apart. Draw direct common tangents to the circle and show that they are equal in length.
Draw a circle of radius 4 cm. Take a point P outside the circle without using the center at the circle. Draw two tangents to the circle from point P.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be ______.
