Given:
AB is the diameter of the circle with center O. ∠AOP = 95°.
Formula Used:
Since ∠AOP is an angle subtended by the diameter, the angle at the circumference subtended by the same arc is half of ∠AOP.
Solution:
Since AB is the diameter, ∠AOP = 95°
triangle OBP is a s implies ∠OBP = ( Because ∠OBP is the exterior angle of triangle OPB and OP = OB both are the radius of this circle so ∠OPB = ∠OBP)
∠OPB+ ∠OBP = 95°
∠OBP =
∠OBP = 47.5°
English
80 Questions
160 Marks
60 Mins English English80 Questions160 Marks60 Mins English English20 Questions40 Marks25 Mins EnglishIn a circle with center O, PQ and RS are two chords. PQ and RS, when produced, meet at point K. If PR is a diameter and ∠ PKS = 66°, what is the value of ∠ QOS?
The perpendicular distance from the center of a circle to a chord is 5 cm. If the length of the chord is 24 cm, find the radius of the circle. Also, calculate the distance of another chord of length 18 cm from the center.
PQ is a chord in the minor segment of a circle and R is a point on the minor arc PQ. The tangents at the points P and Q meet at the point T. If ∠PRQ =102°, then the measure of ∠PTQ is :
A circle is inscribed in a right triangle with legs of length 5 and 12. What is the radius of the circle?
The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?
In a circle, a chord AB is 12 cm long and is at a distance of 4 cm from the center. What is the radius of the circle?
Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?
Two circles with radii 6 cm and 2 cm have their centers 10 cm apart. How many common tangents can be drawn between them, and what type(s) of tangents are they?
A circle with radius x touches another circle with radius 2x externally. What is the length of a direct common tangent?
Two circles with radii r₁ and r₂ touch each other externally. If the length of their direct common tangent is T, which of the following is the correct relationship between T, r₁ and r₂ ?
Suggested Test Series
Suggested Test Series
In a circle with center O, PQ and RS are two chords. PQ and RS, when produced, meet at point K. If PR is a diameter and ∠ PKS = 66°, what is the value of ∠ QOS?
The perpendicular distance from the center of a circle to a chord is 5 cm. If the length of the chord is 24 cm, find the radius of the circle. Also, calculate the distance of another chord of length 18 cm from the center.
PQ is a chord in the minor segment of a circle and R is a point on the minor arc PQ. The tangents at the points P and Q meet at the point T. If ∠PRQ =102°, then the measure of ∠PTQ is :
A circle is inscribed in a right triangle with legs of length 5 and 12. What is the radius of the circle?
The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?
In a circle, a chord AB is 12 cm long and is at a distance of 4 cm from the center. What is the radius of the circle?
Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?
Two circles with radii 6 cm and 2 cm have their centers 10 cm apart. How many common tangents can be drawn between them, and what type(s) of tangents are they?
A circle with radius x touches another circle with radius 2x externally. What is the length of a direct common tangent?
Two circles with radii r₁ and r₂ touch each other externally. If the length of their direct common tangent is T, which of the following is the correct relationship between T, r₁ and r₂ ?
