Topics

# In the given figure, PQ is tangent at A; BC is the diameter. If $$\Large \angle ABC = 42 ^{\circ}.\ then\ \angle PAB$$ is equal to

 A) $$\Large 21 ^{\circ}$$ B) $$\Large 42 ^{\circ}$$ C) $$\Large 48 ^{\circ}$$ D) $$\Large 84 ^{\circ}$$

 C) $$\Large 48 ^{\circ}$$

AP is tangent to the circle at A. Therefore OA and AP are perpendicular to each other.

Therefore, $$\Large \angle OAP = 90 ^{\circ}$$

Again $$\Large OA\ =\ OB$$

Therefore, $$\Large \angle OAB = \angle OBA = 42 ^{\circ}$$

Therefore, $$\Large \angle PAB= \angle PAO - \angle BAO$$

= $$\Large 90 ^{\circ} - 42 ^{\circ} = 48 ^{\circ}$$

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

Similar Questions
1). If length of the tangent from origin to the circle $$\Large x^{2}+y^{2}-26x+K=0\ is\ 5$$, then K is equal to
 A). $$\Large \sqrt{5}$$ B). 5 C). 10 D). 25
2). If area of the given circle is $$\Large 100 \pi$$ square cm, then side of the square inscribed in the circle is
 A). 10 cm B). $$\Large 10\sqrt{2}\ cm$$ C). 20 cm D). $$\Large 20\sqrt{2}\ cm$$
3). The middle points of all chords (each having the same length) of a circle lie on a
 A). rectangle B). square C). circle D). parallelogram
4). Area of the shaded portion in the given figure is $$\Large \left(x = \frac{22}{7}\right)$$
 A). 42 sq. cm B). 48 sq. cm C). 76 sq. cm D). 152 sq. cm
5). A circle A has a radius of 3 cm, two circles B and C have a radius each equal to diameter of the circle A. The radius of a circle D which has an area equal to the total area of A, B and C, is
 A). 9 cm B). 12 cm C). 15 cm D). 18 cm

6). If straight line $$\Large y = x+c$$ is a tangent to the circle $$\Large x^{2}+y^{2}=1$$, then c is equal to
 A). $$\Large \pm \sqrt{2}$$ B). $$\Large \pm 2$$ C). $$\Large \pm 1$$ D). $$\Large \pm 3$$
7). The equation, $$\Large ax^{2}+2hxy+b^{2}+2gx+2fy+c=0$$ represents a circle if
 A). $$\Large h^{2} = ab$$ B). $$\Large a = b$$ C). $$\Large h^{2}+ab = 0$$ D). $$\Large a = b\ and\ h = 0$$
 A). $$\Large \frac{3}{4} \pi r^{2}$$ B). $$\Large \frac{1}{4} \pi r^{2}$$ C). $$\Large \pi r^{2}$$ D). $$\Large 3 \pi r^{2}$$