Advertisements
Advertisements
प्रश्न
A circle is inscribed in ∆ABC having sides 8 cm, 10 cm and 12 cm as shown in the figure, Find AD, BE and CF.
उत्तर
AD = AF = x ...(Tangent of the circle)
BD = BE = y ...(Tangent of the circle)
CE = CF = z ...(Tangent of the circle)
AB = AD + DB
x + y = 12 ...(1)
BC = BE + EC
y + z = 8 ...(2)
AC = AF + FC
x + z = 10 ...(3)
Add (1), (2) and (3)
2x + 2y + 2z = 12 + 8 + 10
x + y + z = `30/2` = 15 ...(4)
By x + y = 12 in (4)
z = 3
y + z = 8 in (4)
x = 7
x + z = 10 in (4)
y = 5
AD = 7 cm, BE = 5 cm and CF = 3 cm
APPEARS IN
संबंधित प्रश्न
The length of the tangent to a circle from a point P, which is 25 cm away from the centre is 24 cm. What is the radius of the circle?
∆LMN is a right angled triangle with ∠L = 90°. A circle is inscribed in it. The lengths of the sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.
PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°. Find ∠OPQ.
O is the centre of the circle with radius 5 cm. T is a point such that OT = 13 cm and OT intersects the circle E, if AB is the tangent to the circle at E, find the length of AB.
Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q, such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.
Draw a tangent at any point R on the circle of radius 3.4 cm and centre at P?
Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.
Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from that point.
Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents.
CP and CQ are tangents to a circle with centre at 0. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is
