QQuestion
The figure shows a circle of radius 9 cm with O as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ.
✓Answer
Radius, OA = OB = 9 cm.
Therefore, diameter AB = OA + OB.
⇒ AB = 9 + 9
⇒ AB = 18 cm
Since PA = 24 cm:
PB = PA − AB
⇒ PB = 24 − 18
⇒ PB = 6 cm
By the tangent-secant theorem:
PQ² = PB × PA
⇒ PQ² = 6 × 24
⇒ PQ² = 144
⇒ PQ = √144
⇒ PQ = 12 cm
Therefore, the length of tangent PQ is 12 cm.
Related Questions
More ICSE Moderate level questions
In the given diagram, an isosceles △ABC is inscribed in a circle with centre O. PQ is a tangent to the circle at C. OM is perpendicular to chord AC and ∠COM = 65°. Find: (a) ∠ABC (b) ∠BAC (c) ∠BCQ
In the given diagram, PS and PT are tangents to the circle. SQ ∥ PT and ∠SPT = 80°. The value of ∠QST is: (a) 140° (b) 90° (c) 80° (d) 50°
In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: (a) 30° (b) 60° (c) 90° (d) 120°
In the given diagram, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is equal to: (a) 40° (b) 30° (c) 60° (d) 90°
In the given diagram, O is the centre of the circle. PR and PT are two tangents drawn from the external point P and touching the circle at Q and S respectively. MN is a diameter of the circle. Given ∠PQM = 42° and ∠PSM = 25°. Find: (a) ∠OQM (b) ∠QNS (c) ∠QOS (d) ∠QMS
In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P. AB = 9 cm, BP = 16 cm, ∠PTB = 50° and ∠OBA = 45°. Find: (a) the length of PT (b) ∠BAT (c) ∠BOT (d) ∠ABT
In the given figure, O is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26°, find: (a) ∠BDA (b) ∠BAD (c) ∠CAD (d) ∠ODB
The letters A, D, M, N, O, S, U and Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter: (a) of the word MONDAY? (b) which does not appear in MONDAY? (c) which appears both in SUNDAY and MONDAY?
Mr Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 − n). Find: (a) its first term and common difference. (b) the sum of its first 25 terms.
The following table gives the duration of movies in minutes: Duration (minutes) Number of movies 100–110 5 110–120 10 120–130 17 130–140 8 140–150 6 150–160 4 Using the step-deviation method, find the mean duration of the movies.
(a) If the lines kx − y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the value of k. (b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (−1, 1).