Advertisements
Advertisements
प्रश्न
In the figure given below, O is the center of the circle and SP is a tangent. If ∠SRT = 65°, find the value of x, y and Z.
उत्तर
TS ⊥ SP,
`=>` ∠TSR = 90°
In ΔTSR,
∠TSR + ∠TRS + ∠RTS = 180°
`=>` 90° + 65° + x = 180°
`=>` x = 180° – 90° – 65°
`=>` x = 25°
Now, y = 2x ...(Angle subtended at the center is double that of the angle subtended by the arc at the same centre)
`=>` y = 2 × 25°
`=>` y = 50°
In ΔOSP,
∠OSP + ∠SPO + ∠POS = 180°
`=>` 90° + z + 50° = 180°
`=>` z = 180° – 140°
`=>` z = 40°
Hence, x = 25°, y = 50° and z = 40°
APPEARS IN
संबंधित प्रश्न
In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 50°, find ∠MQN.
Prove that the lengths of the tangents drawn from an external point to a circle are equal.
From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB = 50°, then find ∠AOB.
Find the area of the shaded region in Fig. 8, where \\
Find the angle between two radii at the centre of the circle as shown in the figure. Lines PA and PB are tangents to the circle at other ends of the radii and ∠APR = 110°.
Construct a pair of tangents to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.
The length of the tangent from an external point on a circle is ______
Draw two concentric circles of radii 2 cm and 3 cm. From a point on the outer circle, construct a pair of tangents to the inner circle.
In the given figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the length of TP.
In the given figure, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5 cm.
