Advertisements
Advertisements
प्रश्न
In the given figure PA = 6, PB = 4 and PC = 8. Find PD
उत्तर
We know that when two chords intersect each other inside a circle, the product of thier segments are equal.
The chords AB and CD intersect at P, so
PA × PB = PC × PD
\[\Rightarrow 6 \times 4 = 8 \times \text{PD}\]
\[ \Rightarrow \text{PD} = \frac{6 \times 4}{8} = 3\]
Thus, PD = 3 units.
APPEARS IN
संबंधित प्रश्न
From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB = 50°, then find ∠AOB.
Prove that a parallelogram circumscribing a circle is a rhombus.
In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.
Find:
- ∠OBD
- ∠AOB
- ∠BED
In the following figure, PQ = QR, ∠RQP = 68°, PC and CQ are tangents to the circle with centre O.
Calculate the values of:
- ∠QOP
- ∠QCP
Find the area of the shaded region in Fig. 8, where \\
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
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
Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.
Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.
Construct a pair of tangents to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.
The length of tangents drawn from an external point to the circle ______
The length of the tangent from an external point on a circle is ______
In a circle of radius 5 cm, AB and AC are the two chords such that AB = AC = 6 cm. Find the length of the chord BC.
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.
In the given figure, if a circle touches the side QR of ΔPQR at S and extended sides PQ and PR at M and N, respectively, then prove that PM = `1/2` (PQ + QR + PR)
In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 6 cm and 8 cm respectively. If the area of ΔABC is 84 cm2, find the lengths of sides AB and AC.
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.
In the given figure, PQ and PR are tangents drawn from P to the circle with centre O such that ∠QPR = 65°. The measure of ∠QOR is ______.
