Advertisements
Advertisements
प्रश्न
In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?
विकल्प
A. 11
B. 10
C. 14
D. 15
उत्तर
Given, AP = 4 cm, BP = 3 cm and AC = 11 cm.
The lengths of tangents drawn from an external point to the circle are equal.
AP = AR, BP = BQ, CQ = CR …….. (1)
AC = 11 cm
⇒ AR + RC = 11 cm
⇒ AP + CQ = 11 cm [From equation (1)]
⇒ 4 cm + CQ = 11 cm
⇒ CQ = (11 − 4) cm
⇒ CQ = 7 cm
BP = BQ = 3 cm
Now, BC = BQ + QC
⇒ BC = (3 + 7) cm
⇒ BC = 10 cm
Hence, the correct option is B.
APPEARS IN
संबंधित प्रश्न
If PT is a tangent at T to a circle whose center is O and OP = 17 cm, OT = 8 cm. Find the length of tangent segment PT.
In the given figure, two tangents RQ, and RP and RP are drawn from an external point R to the circle with centre O. If ∠PRQ =120° , then prove that OR = PR + RQ.
If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.
Use the figure given below to fill in the blank:
Tangent to a circle is _______.
Draw a circle of any radius. Show one diameter, one radius and one chord on that circle.
In the given figure, if ZRPS = 25°, the value of ZROS is ______
If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure. Prove that ∠BAT = ∠ACB
In the following figure, if ∠OAB = 40º, then ∠ACB is equal to ______.
If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C.
