Advertisements
Advertisements
प्रश्न
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.
विकल्प
30º
60º
90º
45º
Advertisements
उत्तर
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to 45º.
Explanation:
We know that, diameter subtends a right angle to the circle.
∴ ∠BCA = 90º ...(i)
Given, AC = BC
⇒ ∠ABC = ∠CAB ...(ii) [Angles opposite to equal sides are equal]
In ΔABC, ∠CAB + ∠ABC + ∠BCA = 180º ...[By angle sum property of a triangle]
⇒ ∠CAB + ∠CAB + ∠90º = 180º ...[From equations (i) and (ii)]
⇒ 2∠CAB = 180º – 90º
⇒ ∠CAB = `(90^circ)/2`
∴ ∠CAB = 45º
APPEARS IN
संबंधित प्रश्न
In the given figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects PQ at A and RS at B. Prove that ∠AOB = 90º
PA and PB are tangents from P to the circle with centre O. At point M, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN.
Write True or False. Give reason for your answer.
Line segment joining the centre to any point on the circle is a radius of the circle.
Write True or False. Give reasons for your answers.
If a circle is divided into three equal arcs, each is a major arc.
Fill in the blank:
An arc is a ................ when its ends are the ends of a diameter.
In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.
Find the length of the chord of a circle in the following when:
Radius is 1. 7cm and the distance from the centre is 1.5 cm
In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC at P and OA at Q.
Prove that:
( i ) ΔOPA ≅ ΔOQC
( ii ) ΔBPC ≅ ΔBQA
In the adjoining figure ‘O’ is the center of the circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB?
If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC.
