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 3 cm. Draw a pair of tangents to this circle, which are inclined to each other at an angle of 60º.
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.
Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.
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.
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.
Draw an isosceles triangle with sides 6 cm, 4 cm, and 6 cm. Construct the incircle of the triangle. Also, write the steps of construction.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°. It is required to draw tangents at the end points of those two radii of the circle, the angle between which is ______.
Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.
Construct a pair of tangents to a circle of radius 4 cm from a point P lying outside the circle at a distance of 6 cm from the centre.
Draw a circle of radius 2.5 cm. Construct a pair of tangents from a point Pat a distance of 6 cm from the centre of the circle.
