Advertisements
Advertisements
प्रश्न
Draw a circle of radius 3 cm and draw chord XY 5 cm long. Draw the tangent of the circle passing through point X and point Y (without using the center of the circle)
उत्तर
Analysis:
As shown in the figure, line l, m are the tangents to the circle at points Y, X respectively.
seg XY is a chord of the circle and ∠XAY is an inscribed angle. By tangent secant angle theorem,
∠XAY = ∠YXM and ∠XAY = ∠XYM
By converse of tangent secant angle theorem,
If we draw ∠XYM such that ∠XAY = ∠XYM, then ray YM
i.e. (line l) is a tangent at point Y.
Also, if we draw ∠YXM such that ∠XAY = ∠YXM, then ray XM.
i.e. (line m) is a tangent at point X.
Steps of construction:
- Draw a circle of radius 3 cm.
- Draw a chord XY of length 5 cm.
- Take a point A on the major arc, other than X and Y.
- Join XA and YA.
- Using X and Y as vertices and chord XY as one side, draw ∠XYM and ∠YXM equal to ∠XAY.
- Lines containing the rays XM and YM are the tangents to the circle at X and Y respectively.
APPEARS IN
संबंधित प्रश्न
Draw a tangent at any point ‘P’ on the circle of radius 3.5 cm and centre O.
Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.
Select the correct alternative for the following question.
The number of tangents that can be drawn to a circle at a point on the circle is ............... .
Select the correct alternative for the following question.
The maximum number of tangents that can be drawn to a circle from a point out side it is .............. .
Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.
Complete the following activity to draw a tangent to a circle at a point on the circle.
Draw a circle of radius 2.2 cm with O as centre.
↓
Take any point P on the circle and draw ray OP.
↓
Draw a perpendicular line to the ray at point P.
↓
Name the perpendilcular line as l
l is the tangent at point P.
Choose the correct alternative:
The tangents drawn at the end of a diameter of a circle are ______
Choose the correct alternative:
Which theorem is used while constructing a tangent to the circle by using center of a circle?
| Draw a circle and take any point P on the circle. Draw ray OP |
| ↓ |
| Draw perpendicular to ray OP from point P |
| Draw a circle with center O and radius 3 cm |
| ↓ |
| Take any point P on the circle |
| ↓ |
| Draw ray OP |
| ↓ |
| Draw perpendicular to ray OP from point P |
Draw a circle of radius 3.4 cm, take any point P on it. Draw tangent to the circle from point P
Draw a circle of radius 3 cm. Take any point K on it. Draw a tangent to the circle from point K without using center of the circle.
Draw a circle of radius 3.4 cm. Draw a chord MN 5.7 cm long in a circle. Draw a tangent to the circle from point M and point N
Draw a circle with center C and radius 3.2 cm. Draw a tangent to the circle from point P at a distance of 7.5 cm from the center of the circle
Draw a circle of radius 4.2 cm. Draw arc PQ measuring 120°. Draw a tangent to the circle from point P and point Q
Draw a circle with center O and radius 3 cm. Take the point P and the point Q at a distance of 7 cm from the center of the circle on the opposite side of the circle such that their line of intersection passing through the center of the circle Draw a tangent to the circle from the point P and the point Q
Draw a circle with center O and radius 2.8 cm. Take point P in the exterior of a circle such that tangents PA and PB drawn from point P make an angle ∠APB of measure 70°
Draw a circle of suitable radius. Take point T on it. Draw a tangent through point T.
