Advertisements
Advertisements
प्रश्न
In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.
Advertisements
उत्तर
In the given figure, TS ⊥ SP,
m∠TSR = m∠OSP = 90°
In `triangle TSR, m angleTSR + m angleTSR + m angle RTS = 180^@`
`=> 90^@ + 65^@ + x = 180^@`
`=> x = 180^@ - 90^@ - 65^@`
`=> x= 25^@`
Now, y = 2x [Angle subtended at the centre is double that of the angle subtended by the arc at the same centre]
`=> y = 2 xx 25^@`
`:. y = 50^@`
In `triangle OSP ,m angleOSP + m angle SPO + m angle POS =180^@`
`=> 90^@ + z + 50^@ = 180^@`
`=> z = 180^@ - 140^@`
`:. z=40^@`
APPEARS IN
संबंधित प्रश्न
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 a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.
Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.
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 triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.
- Construct a circle circumscribing the triangle ABC.
- Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
Draw a circle with center O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.
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 form the centre of the other circle.
Draw a circle of radius 4.2. Draw a pair of tangents to this circle inclined to each other at an angle of 45°
Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°.
Draw a circle at a radius of 3 cm. Take a point at 5.5 cm from the center at the circle. From point P, draw two tangents to the circle.
