Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.
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 of radius 3 cm. Take a point at a distance of 5.5 cm from the centre of the circle. From point P, draw two tangents to the circle.
In the given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. if ∠BAQ = 30°. Prove that:
- BD is a diameter of the circle.
- ABC is an isosceles triangle.
Draw a circle of radius 3.5 cm. Take two points A and B on one of its extended diameter, each at a distance of 5 cm from its center. Draw tangents to the circle from each of these points A and B.
Using ruler and compasses only, draw tangents to a circle of radius 3 cm from a point 5 cm from the centre. What is the length of each of them ?
Draw two circles of radii 2.5 cm and 3.5 cm respectively so that their centres are 8 cm apart. Draw direct comm on tangents to the circle.
In Figure 2, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.
A pair of tangents can be constructed from a point P to a circle of radius 3.5cm situated at a distance of ______ from the centre.
Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.
