Advertisements
Advertisements
Questions
In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.
In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find the length of seg PS.
Solution
Using tangent secant segments theorem, we have
PQ2 = PR × PS
∴ (12)2 = 8 × PS
PS = `144/8`
= 18 units
∴ RS = PS − PR
= 18 − 8
∴ RS = 10 units
Notes
Students should refer to the answer according to the question.
RELATED QUESTIONS
If two circles with radii 8 cm and 3 cm, respectively, touch internally, then find the distance between their centers.
If two circles with radii 8 cm and 3 cm respectively touch externally, then find the distance between their centres.
Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres
If radii of two circles are 4 cm and 2.8 cm. Draw a figure of this circles touching each other externally.
In the given figure, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively. Prove that – (1) seg AP || seg BQ,
(2) ∆APR ~ ∆RQB, and
(3) Find ∠ RQB if ∠ PAR = 35°
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle?
Four alternative answers for the following question is given. Choose the correct alternative.
A circle touches all sides of a parallelogram. So the parallelogram must be a, ______
Line l touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.
- What is d(O, P) = ? Why?
- If d(O, Q) = 8 cm, where does the point Q lie?
- If d(O, Q) = 15 cm, How many locations of point Q are line on line l? At what distance will each of them be from point P?
How many common tangents can be drawn to two circles which touch each other internally?
(A) One (B) Two (C) Three (D) Four
In the given figure, circle with centre M touches the circle with centre N at point T. Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR.
(1) Find the length of segment MT
(2) Find the length of seg MN
(3) Find the measure of ∠NSM.
In the given figure, circles with centres C and D touch internally at point E. D lies on the inner circle. Chord EB of the outer circle intersects inner circle at point A. Prove that, seg EA ≅ seg AB.
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles having diameters 8 cm and 6 cm touch each other internally. Find the distance between their centres.
Line ℓ touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.
If d(O, R) = 15 cm, how many locations of point R are line on line l? At what distance will each of them be from point P?
Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.
