Advertisements
Advertisements
प्रश्न
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 ?
उत्तर
In the given figure, we have an external point X from where two tangents, XP and XQ, are drawn to the circle.
XP = XQ (The lengths of the tangents drawn from an external point to the circle are equal.)
Similarly, we have:
AP = AR
BQ = BR
Now, XP = XA + AP ...(1)
XQ = XB + BQ ...(2)
On putting AP = AR in equation (1) and BQ = BR in equation (2), we get:
XP = XA + AR
XQ = XB + BR
Since XP and XQ are equal, we have:
XA + AR = XB + BR
Hence, proved.
APPEARS IN
संबंधित प्रश्न
In the given circle with centre O, ∠ABC = 100°, ∠ACD = 40° and CT is a tangent to the circle at C. Find ∠ADC and ∠DCT.
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 3, a right triangle ABC, circumscribes a circle of radius r. If AB and BC are of lengths of 8 cm and 6 cm respectively, find the value of r.
In Figure 5, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of ΔPQR = 189 cm2, then find the lengths of sides PQ and PR.
The length of the direct common tangent to two circles of radii 12cm and 4cm is 15cm. calculate the distance between their centres.
Calculate the length of direct common tangent to two circles of radii 3cm and Bern with their centres 13cm apart.
In the figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA + AR = XB + BR.
If PA and PB are two tangents drawn from a point P to a circle with center C touching it A and B, prove that CP is the perpendicular bisector of AB.
In figure, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = `6sqrt(3)`, then find
(i) Radius of the circle.
(ii) Measures of ∠K and ∠M.
In the given figure O, is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26° find:
- ∠BDA
- ∠BAD
- ∠CAD
- ∠ODB
