Advertisements
Advertisements
प्रश्न
Two circles touch externally at a point P. from a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and E respectively. Prove that TQ = TR.
उत्तर
Let the circles be represented by (i) & (ii) respectively
TQ, TP are tangents to (i)
TP, TR are tangents to (ii)
We know that
The tangents drawn from external point to the circle will be equal in length.
For circle (i), TQ = TP …. (i)
For circle (ii), TP = TR …. (ii)
From (i) & (ii) TQ = TR
APPEARS IN
संबंधित प्रश्न
From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
ABCD is a quadrilateral such that ∠D = 90°. A circle (O, r) touches the sides AB, BC, CD and DA at P,Q,R and If BC = 38 cm, CD = 25 cm and BP = 27 cm, find r.
The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4cm,5cm and 7cm respectively. Determine the length of fourth side.
On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m(∠ACB) and m (∠ABC).
A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is
State, if the following statement is true or false:
If the end points A and B of the line segment lie on the circumference of a circle, AB is a diameter.
In the adjoining figure, seg DE is the chord of the circle with center C. seg CF⊥ seg DE and DE = 16 cm, then find the length of DF?
From the figure, identify a diameter.
A circle of radius 3 cm with centre O and a point L outside the circle is drawn, such that OL = 7 cm. From the point L, construct a pair of tangents to the circle. Justify LM and LN are the two tangents.
In the adjoining figure, AC is a diameter of the circle. AP = 3 cm and PB = 4 cm and QP ⊥ AB. If the area of ΔAPQ is 18 cm2, then the area of shaded portion QPBC is ______.
