Advertisements
Advertisements
प्रश्न
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is ______.
विकल्प
12 cm
13 cm
8.5 cm
`sqrt119` cm
उत्तर
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is `bbunderline(sqrt119 cm)`.
Explanation:
Suppose there is a circle whose center is O.
In right ΔQPO,
According to Pythagoras theorem,
OQ2 = OP2 + PQ2
= PQ = `sqrt(OQ^2 - OP^2)`
= PQ = `sqrt(12^2 - 5^2)`
= PQ = `sqrt(144 - 25`
= PQ = `sqrt119` cm.
APPEARS IN
संबंधित प्रश्न
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of `(DO')/(CO')`
A tangent to a circle intersects it in ______ point (s).
In fig. 5 is a chord AB of a circle, with centre O and radius 10 cm, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence find the area of major segment ALBQA. (use π = 3.14)
In Figure 2, XP and XQ are two tangents to the circle with centre O, drawn from an external point X. ARB is another tangent, touching the circle at R. Prove that XA + AR = XB + BR ?
In the given Figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°. Then ∠BOC is equal to ______
If Δ ABC is isosceles with AB = AC and C (O, r) is the incircle of the ΔABC touching BC at L,prove that L bisects BC.
In following figure , the incircle of Δ ABC , touches the sides BC , CA and AB at D , E and F respectively. Show AF + BD + CE = AE + BF + CD
In the given figure, 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 AB.
In the following figure, PQ is the tangent to the circle at A, DB is a diameter and O is the centre of the circle. If ∠ ADB = 30° and ∠ CBD = 60° ; calculate ∠ PAD.
In the alongside, figure, O is the centre of the circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80° and ∠XOZ = 140°. Calculate the value of ∠ZXY.
In figure, if ∠AOB = 125°, then ∠COD is equal to ______.
In the figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to ______.
In figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.
In the given figure, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠AOP = 60°, then find ∠C.
The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is ______.
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° ∠OBA = 45°
Find:
- Length of PT
- ∠BAT
- ∠BOT
- ∠ABT
In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of ∠BAC is ______.
In the given diagram an isosceles ΔABC 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:
- ∠ABC
- ∠BAC
- ∠BCQ
In the adjoining diagram, O is the centre of the circle and PT is a tangent. The value of x is ______.
