Tangents To A Circle
Muhtasari
A tangent just grazes a circle, touching it at a single point. There is one beautiful fact that makes every tangent question solvable: the tangent is perpendicular to the radius drawn to the point where they touch. That right angle is the key that unlocks the equation of the tangent.
In this lesson you will use the radius-tangent right angle, together with the gradient rules you already know, to find the equation of a tangent at a given point on a circle, without any calculus. Find the gradient of the radius, take its negative reciprocal, and you have the gradient of the tangent.
Malengo
- Solve problems involving tangents to a circle, including finding the equations of tangents (no use of calculus is expected).
Maelezo ya Somo
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Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Tathmini ya Somo
Hongera kwa kukamilisha somo la Tangents To A Circle. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- A tangent to a circle is perpendicular to which line at the point of contact? A. The diameter through the centre only B. The radius at that point C. Any chord D. The x-axis Answer: B
- A circle has centre O(0,0) and passes through P(3,4). What is the gradient of the radius OP? A. 3/4 B. 4/3 C. -3/4 D. -4/3 Answer: B
- For the same circle, what is the gradient of the tangent at P(3,4)? A. 4/3 B. 3/4 C. -3/4 D. -4/3 Answer: C
- The equation of the tangent at P(3,4) to the circle centre O(0,0) is: A. y = (4/3)x B. y = -(3/4)x + 25/4 C. y = (3/4)x + 4 D. y = -(4/3)x + 8 Answer: B
- A circle has centre C(1,2) and passes through P(4,6). The tangent gradient at P is: A. 4/3 B. 3/4 C. -3/4 D. -4/3 Answer: C
Inapatikana kwenye programu ya Green Bridge
Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Inapatikana kwenye programu ya Green Bridge
Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Vitabu Vinavyopendekezwa
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Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Tangents To A Circle? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.
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