Advertisements
Advertisements
Question
In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find:
1) AB.
2) the length of tangent PT.
Advertisements
Solution
Theorem used: Product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
1) As chord CD and tangent at point T intersect each other at P,
`PC xx PD = PT^2` ...(i)
AB is the diameter and tangent at point T intersect each other at P,
`PA xx PB = PT^2` ...(ii)
From (i) and (ii), PC × PD = PA × PB … (iii)
Given: PD = 5cm, CD = 7.8 cm
PA = PB + AB = 4 + AB, and PC = PD + CD = 12.8 cm
Subs. these values in (iii),
12.8 × 5 = (4 + AB) × 4
`=> 4 + AB = (12.8 xx 5)/4`
`=> 4 + AB = 16`
`=> AB = 12cm`
2) `PC xx PD = PT^2`
`=> PT^2 = 12.8 xx 5 =64`
`=> PT = 8 cm`
Thus, the length of the tangent is 8 cm
APPEARS IN
RELATED QUESTIONS
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 line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from 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°
Write the steps of construction for drawing 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 of radius 32 cm. Draw a tangent to the circle making an angle 30° with a line passing through the centre.
Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Use ruler and compass only for answering this question.
Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.
Measure and write down the length of any one tangent.
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.
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 ______.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be ______.
