From a point A outside a circle with centre O, a tangent AB is drawn to the circle. The circle's radius measures 6 cm, and the tangent segment AB has a length of 8 cm. Find the distance between point A and the centre O of the circle.
10 cm
A tangent to a circle is perpendicular to the radius drawn to the point of contact, so \(OB \perp AB\) where B is the point of contact.
Therefore triangle OBA is right-angled at B, with OB the radius and AB the tangent.
Here the radius \(OB = 6\) cm and the tangent \(AB = 8\) cm.
By the Pythagoras theorem, \(OA^2 = OB^2 + AB^2\).
Substituting: \(OA^2 = 6^2 + 8^2 = 36 + 64 = 100\).
So \(OA = \sqrt{100} = 10\) cm.
The distance between point A and the centre O is 10 cm.
Similar Questions
A chord AC subtends an angle of 90° at the center O. If the radius of the circle is 8 cm, what is the length of the chord AC?
Two chords, AB and CD, cross at point P inside a circle. Segments AP, PB, and CP have lengths of 6 cm, 8 cm, and 4 cm, respectively. How long is the chord CD in total?
From a point outside a circular garden, two tangents of length 15 m each are drawn. If the radius of the garden is 9 m, find the distance from the point to the center.
The angle subtended by a chord at the circumference is $35^\circ$. The angle subtended at the center is:
The angle subtended by the diameter at any point on the circle is:
The number of circles that can pass through two fixed points is:
A circle has a radius of 17 cm. Two of its chords are parallel and separated by a distance of 23 cm. If the length of one of these chords is 30 cm, find the length of the second chord.
Two circles with centers C₁ and C₂ have radii r₁ = 8 cm and r₂ = 7 cm, respectively. The distance between their centers is 17 cm. A common internal tangent touches the circles at points P₁ and P₂. What is the length of the segment P₁P₂?
In a circle with center O, AC is a chord. OB is perpendicular to AC, and B is the midpoint of AC. If the angle ∠AOC = 120°, and the radius of the circle is 10 cm, what is the length of the chord AC?
In a circle with a radius of 15 cm, a chord measures 18 cm in length. Find the perpendicular distance from the center of the circle to this chord.
Important Questions from Circles, Chords and Tangents
AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 112°, then what is the measure of ∠OAB ?
The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?
An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?
What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?
There are two identical circles of radius 10 cm each. If the length of the direct common tangent is 26 cm, then what is the length (in cm) of the transverse common tangent?
