Advertisements
Advertisements
प्रश्न
In Figure 1, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, find x.
(A) 10
(B) 9
(C) 8
(D) 7
उत्तर
Given:
BC = 7 cm
CR = 3 cm
AS = 5 cm
AB = x cm
Now, BQ = BP (The lengths of the tangents drawn from an external point to a circle are equal.)
AP = AS = 5 cm ...(1)
Similarly, we have:
CR = CQ = 3 cm
BQ = BC \[-\] CQ and BC = 7 cm (Given)
⇒ BQ = BP = 4 cm ...(2)
AB = AP + PB = (5 + 4) cm = 9 cm
⇒ x = 9 cm
Hence, the correct option is B.
APPEARS IN
संबंधित प्रश्न
Prove that “The lengths of the two tangent segments to a circle drawn from an external point are equal.”
In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 50°, find ∠MQN.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.
Find the angle between two radii at the centre of the circle as shown in the figure. Lines PA and PB are tangents to the circle at other ends of the radii and ∠APR = 140°.
Two concentric circles are of radii 5 cm and 3 cm. Length of the chord of the larger circle, (in cm), which touches the smaller circle is
(A) 4
(B) 5
(C) 8
(D) 10
M and N are the midpoints of chords AB and CD . The line MN passes through the centre O . Prove that AB || CD.
PA and PB are the two tangents drawn to the circle. O is the centre of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠OPA = 35°, then ∠POB = ______
The angle between two tangents to a circle may be 0°.
Draw two concentric circles of radii 2 cm and 3 cm. From a point on the outer circle, construct a pair of tangents to the inner circle.
Draw two concentric circles of radii 2 cm and 5 cm. From a point P on outer circle, construct a pair of tangents to the inner circle.
