Mathematics
In the adjoining figure, sides BC, CA and AB of △ABC touch a circle at point D, E and F respectively. If BD = 4 cm, DC = 3 cm and CA = 8 cm, then the length of side AB is
12 cm
11 cm
10 cm
9 cm
Answer
We know that if two tangents are drawn from an external point to a circle then, the lengths of the tangents are equal.
∴ BF = BD = 4 cm, CE = CD = 3 cm and AF = AE.
Given, CA = 8 cm.
From figure,
⇒ CA = AE + CE
⇒ 8 = AE + 3
⇒ AE = 8 - 3 = 5 cm.
We know AF = AE = 5cm.
From figure,
AB = AF + BF = 5 + 4 = 9 cm.
Hence, Option 4 is the correct option.
Related Questions
In the adjoining figure, PA and PB are tangents to a circle with centre O. If ∠APB = 50°, then ∠OAB is equal to
25°
30°
40°
50°
In the adjoining figure, O is the centre of a circle and PQ is a chord. If the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is
100°
80°
90°
75°
PQ is a tangent to a circle at point P. Centre of circle is O. If △OPQ is an isosceles triangle, then ∠QOP is equal to
30°
60°
45°
90°
In the adjoining figure, sides BC, CA and AB of △ABC touch a circle at the points P, Q and R respectively. If PC = 5 cm, AR = 4 cm and RB = 6 cm, then the perimeter of △ABC is
60 cm
45 cm
30 cm
15 cm
