Advertisements
Advertisements
प्रश्न
In Figure 5, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR =12 cm. Find the lengths of QM, RN and PL ?
उत्तर
Given: In ΔPQR, PQ = 10, QR = 8 cm and PR = 12 cm.
We know that, the lengths of tangents drawn from an external point to a circle are equal.
∴ QM = OL = x (Say)
RM = RN = y (Say)
PL = PN = z (Say)
QR = QM + MR = x + y = 8 cm ……(1)
PQ = PL + LQ = z + x = 10 cm ……(2)
PR = PN + NR = z + y = 12 cm ……(3)
Adding (1), (2) and (3) , we have
(x + y) + (z + x) + (z + y) = (8 + 10 + 12) = 30 cm
∴ 2(x + y + z) = 30 cm
⇒ x + y + z = 15 cm …..(4)
From (2) and (4), we have
10 + y = 15
∴ y = 5
From (3) and 4, we have
12 + x = 15
∴ x = 3
From (1) and (4), we have
⇒ z + 8 = 15
⇒ z = 7
∴ QM = x = 3 cm
RN = y = 5 cm
PL = z = 7 cm
APPEARS IN
संबंधित प्रश्न
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.
In the following figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π =]`22/7` [CBSE 2014]
In the following figure, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. (Use π = 22/7)
In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park.
If the numerical value of the area of a circle is equal to the numerical value of its circumference , find its radius.
The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then ______.
The radius of a circular wheel is 42 cm. Find the distance travelled by it in :
(i) 1 revolution ;
(ii) 50 revolutions ;
(iii) 200 revolutions ;
Find the area of the dining table whose diameter is 105 cm
A table top is semicircular in shape with diameter 2.8 m. Area of this table top is ______.
