Circles — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Circles (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "A circle has radius 5 cm. A tangent is.
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A circle has radius 5 cm. A tangent is drawn from an external point P such that the length of tangent is 12 cm. Find the distance from P to the center of the circle.
Answer
Step 1: Draw diagram - Circle with center O, radius = 5 cm, tangent PT = 12 cm Step 2: Use tangent property - Tangent is perpendicular to radius at point of contact Step 3: Apply Pythagoras theorem in…
From point A outside a circle, two tangents AB and AC are drawn. If AB = 8 cm and ∠BAC = 60°, find the radius of the circle.
Answer
Step 1: Given - AB = AC = 8 cm (tangents from external point are equal), ∠BAC = 60° Step 2: In triangle ABC, AB = AC, so it's isosceles ∠ABC = ∠ACB = (180° - 60°)/2 = 60° Therefore, triangle ABC…
A chord PQ of length 16 cm is at a distance of 6 cm from the center of a circle. Find the radius of the circle.
Answer
Step 1: Draw perpendicular from center O to chord PQ, meeting at M Step 2: Perpendicular from center bisects the chord PM = MQ = 16/2 = 8 cm Step 3: Given - OM = 6 cm (distance from center to chord…
Two concentric circles have radii 3 cm and 5 cm. A chord of the outer circle touches the inner circle. Find the length of this chord.
Answer
Step 1: Let O be common center, AB be chord of outer circle touching inner circle at P Step 2: Since AB touches inner circle at P, OP ⊥ AB OP = radius of inner circle = 3 cm Step 3: OP bisects chor…
When do you use the formula: (Length of tangent)² = (Distance from external point)² - (Radius)²?
Answer
Use this formula when: - Finding tangent length from an external point - Given distance from external point to center and radius Example: Point P is 13 cm from center O of a circle with radius 5 cm T…
Prove that tangents drawn from an external point to a circle are equal in length.
Answer
Given: Circle with center O, external point P, tangents PA and PB To prove: PA = PB Proof: Step 1: Join OP, OA, OB Step 2: ∠OAP = 90° (tangent ⊥ radius) ∠OBP = 90° (tangent ⊥ radius) Step 3: In ri…
A quadrilateral ABCD is circumscribed about a circle. If AB = 6 cm, BC = 7 cm, CD = 4 cm, find AD.
Answer
Step 1: For a quadrilateral circumscribed about a circle (tangential quadrilateral): Sum of opposite sides are equal AB + CD = BC + AD Step 2: Substitute given values: 6 + 4 = 7 + AD 10 = …
In a circle with center O, chord AB = 12 cm and chord CD = 16 cm. If AB is 8 cm from center, find the distance of CD from center.
Answer
Step 1: For chord AB - let M be foot of perpendicular from O OM ⊥ AB, so AM = MB = 12/2 = 6 cm Given: OM = 8 cm Step 2: Find radius using right triangle OMA: OA² = OM² + AM² OA² = 8² + 6² …
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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