Advertisements
Advertisements
Question
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
Options
`sqrt(21)` cm
`3sqrt(21)` cm
`2sqrt(21)` cm
`4sqrt(21)` cm
Advertisements
Solution
`2sqrt(21)` cm
Explanation:
The line from the centre to the tangent is perpendicular to the tangent.
∴ CS ⊥ ST
So, in right angled ΔCST, by the Pythagoras theorem,
CT2 = CS2 + ST2
(10)2 = (4)2 + ST2
ST2 = 100 – 16 = 84
⇒ ST = `2sqrt(21)`
Thus, the length of ST is `2sqrt(21)` cm.
APPEARS IN
RELATED QUESTIONS
A man goes 10 m due east and then 24 m due north. Find the distance from the starting point
A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(A)\[7 + \sqrt{5}\]
(B) 5
(C) 10
(D) 12
Find the side and perimeter of a square whose diagonal is 10 cm.
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.
Find the side of the square whose diagonal is `16sqrt(2)` cm.
In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :
(i) AC
(ii) CD
In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.
A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.
A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that OB2 + OD2 = OC2 + OA2
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9AQ2 = 9AC2 + 4BC2
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?
Find the unknown side in the following triangles
From given figure, In ∆ABC, If AC = 12 cm. then AB = ?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle.
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
If ΔABC ~ ΔPQR, `("ar" triangle "ABC")/("ar" triangle "PQR") = 9/4` and AB = 18 cm, then the length of PQ is ______.
In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is ______.
Two squares having same perimeter are congruent.
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.
