Question

A line is drawn 7 units for the center of circle A to a point B outside the circle. If a line is drawn from B to tangent point C, what is the length of line BC.

Answer 1

OQ is 25 cm.

In a circle, if a tangent is drawn at a point P and a line through the center O of the circle is drawn to intersect the tangent at point Q, then the line segment OQ is a radius of the circle.

Given that the radius of the circle is 7 cm, and PQ is the tangent segment with a length of 24 cm, you can use the Pythagorean Theorem to find OQ.

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, OQ is the hypotenuse, and OP and PQ are the other two sides. Therefore:

OQ^2 =OP^2 +PQ^2

Substitute the given values:

OQ^2 =7^2 +24^2

OQ^2 =49+576

OQ^2 =625

Now, take the square root of both sides to solve for OQ:

OQ= 625

OQ=25

So, OQ is 25 cm.

Question

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.