Advertisements
Advertisements
Question
In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of ∠AQB is ______.
Options
`62 (1/2)^circ`
125°
55°
90°
Solution
In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of ∠AQB is `underlinebb(62 (1/2))^circ`.
Explanation:
Given, ∠APB = 55°
∴ ∠ACB = 180° – 55° = 125° ...`((∵ ∠APB and ∠ACB "are"),("supplementary angles"))`
Now, as we know that
Angle subtended by an arc at the centre = 2 × angle subtended by arc at any point on the remaining part of the circle
∴ 125° = 2 × ∠AQB
`\implies` ∠AQB = `125/2`
= 62.5° or `62 (1/2)^circ`
APPEARS IN
RELATED QUESTIONS
In the below given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If∠PRQ = 120°, then prove that OR = PR + RQ.
In the following Fig, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA.
If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR = 120°, prove that 2PQ = PO.
In the given circle with center o, ∠ABC=100°, ∠ACD=40° and CT is tangent to the circle at C. find ∠ADC and ∠DCT.
In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.
Find: ∠BED
The number of tangents drawn at a point of the circle is/are ______
In the given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 6 cm then the length of BR is ______
If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then OP = `asqrt(2)`.
In the given figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the length of TP.
From a point P, the length of the tangent to a circle is 24 cm and the distance of P from the centre of the circle is 25 cm. Find the radius of the circle.
