CBSE Class 10 Mathematics Basic 2024: question 25

Hints

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Step-by-step solution

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1. Figure: a circle with centre O and diameter AB. Tangent $l$ is drawn at A and tangent $m$ at B. Let $\angle 1$ be the angle between OA and $l$, and $\angle 2$ be the angle between OB and $m$, on opposite sides of AB. To prove: $l\parallel m$.

   ½ mark

2. $\angle 1=90^{\circ }$ and $\angle 2=90^{\circ }$ [tangent ⟂ radius at the point of contact]. So $\angle 1=\angle 2$.

   1 mark

3. $\angle 1$ and $\angle 2$ are alternate interior angles made by the transversal AB with lines $l$ and $m$. Since they are equal, $l\parallel m$.

   ½ mark

Answer: The tangents at the ends of a diameter are parallel (alternate angles, each 90°, are equal)

Revise the chapter

• Chapter: Circles (notes, formulas, where marks are lost and every past question)
• Topic: Solving Problems Using Tangent Properties