Circles

$$Chord$$

A chord is a straight line segment that connects any two distinct points on the circumference of a circle. It's a fundamental element in circle geometry.

$$\tan gent$$

A tangent to a circle is a straight line that intersects (touches) the circle at precisely one point. This point is known as the point of tangency or the point of contact.

$$Secant$$

A secant is a straight line that passes through a circle, intersecting it at precisely two distinct points.

$$True$$

$$True$$

△OQP and △ORP are congruent by the RHS

since OQ = OR as radii,

OP is common,

and Angle Q = Angle R = 90°

Therefore,

$$\angle OPR=\angle OPQ$$

$$∠QOP=∠ROP$$

$$True$$

Two chords of a circle are equal if the perpendiculars drawn from the centre to them are equal.

$$True$$


The definition of a tangent is a line that intersects a circle at exactly one point (the point of tangency). If you attempt to draw a second, distinct line that also touches the circle only at that exact same point, the second line would necessarily intersect the first line and would either:

1. Be the exact same line (not a second tangent), or

2. If slightly rotated, it would cut through the circle, making it a secant line instead of a tangent.

$$True$$

The statement refers to the Angle Sum Property of a Triangle.

This property is a fundamental theorem in geometry, stating that the sum of the three interior angles of any Euclidean triangle is always $$180\degree$$

$$Isosceles$$

This is because the Two Tangent Theorem states that the two tangent segments drawn from the external point T to the circle, TA and TB, must be equal in length (TA=TB). Any triangle with at least two equal sides is, by definition, an isosceles triangle.

$$Supplementary$$

Since $$\angle OAP=\angle OBP=90\degree$$