Advertisements
Advertisements
प्रश्न
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.
पर्याय
`sqrt(21)` cm
`3sqrt(21)` cm
`2sqrt(21)` cm
`4sqrt(21)` cm
Advertisements
उत्तर
`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
संबंधित प्रश्न
Two towers of heights 10 m and 30 m stand on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
In ΔABC, Find the sides of the triangle, if:
- AB = ( x - 3 ) cm, BC = ( x + 4 ) cm and AC = ( x + 6 ) cm
- AB = x cm, BC = ( 4x + 4 ) cm and AC = ( 4x + 5) cm
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ2 + BP2) = (AB2 + PQ2)
Prove that (1 + cot A - cosec A ) (1 + tan A + sec A) = 2
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
Choose the correct alternative:
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals ______.
Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is ______.
