In Fig. $6.61$, two chords $\mathrm{AB}$ and $\mathrm{CD}$ intersect each other at the point $\mathrm{P}$. Prove that :
(i) $\Delta \mathrm{APC}-\Delta \mathrm{DPB}$
(ii) $\mathrm{AP} . \mathrm{PB}=\mathrm{CP} . \mathrm{DP}$

Answer

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Geometry

NCERT Class 10 - Math

Chapter 6

Triangles

Section 6

Pythagoras Theorem

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Video Transcript

we have to call a number seven. In this we have two cars, A. B. And city of a a circle which intercepts each other at point B. So we need to prove two things. Let us draw the circle. Oh, key. Uh There are two cars. Let us say A. B. And cd. See and D. So it is being given. Okay. Intersecting at B. Yeah. We have to do two Things 1st. We need to prove, Yeah. Single A. Pc is similar to jangle DP and B. If you support the single to be won the single to be too. I'm not this because we'll be using although property of the circle course of a circle. So we have angle one equal to angle to because angle it is made in the same segment. Okay. And anger Abc will be put to anger B. B. B. A. Pc. This angle should be called this angle because particularly opposed angle. So they can easily prove that strangle a Pc will be similar to triangle Dp. B angle angle similarity. Okay. And problems 2nd. Ah Question Second was ap into P. B. Equal to seep into D. P. No, if these two triangles are similar, so we should write A P. By P. C. Equal to D. P. By B. B. Corresponding side should be in proportion. So A. Being too B. b. equals two Bc. And two Bp. But this is the thing we need to prove and let us list uh see that there's a pc. So put Britain SCP. Not worried about it.

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